Fluid Mechanics

Consider the following relationship between the shear stress and the rate of shear strain $ \tau = \mu \left(\frac{du}{dy}\right)^n $. When the exponent n is greater than 1, the fluid is known as

What is the pressure difference between inside and outside of a droplet of water?

A floating body has centre of buoyancy at B, centre of gravity at G and metacentre at M. Then for stable equilibrium of the body

At the point of boundary layer separation

If x is the distance from the leading edge of a plate, then thickness of laminar boundary layer varies as

The velocity profile of a fully developed laminar flow in a straight circular pipe is given by the expression $ u(r) = -\frac{R^2}{4\mu} \left(\frac{dp}{dx}\right) \left[1 - \frac{r^2}{R^2}\right] $ where $ \frac{dp}{dx} $ is constant and the symbols have their usual meanings. The average velocity of fluid in the pipe is

A jet of water impinges with velocity v on a plate which is inclined at angle $ \alpha $ with the direction of jet. The force exerted on the plate in a direction normal to flow is

A vessel contains oil (density 0.8 $ g/cm^3 $) over mercury (density 13.6 $ g/cm^3 $). A homogeneous sphere floats with half its volume immersed in mercury and the other half is in oil. The density of the material of the sphere in $ g/cm^3 $ is

Euler's dimensionless number relates

What is the dimension of kinematic viscosity of a fluid?

State the Newton's law of viscosity. Explain the effect of temperature on viscosity of water and that of air.

Define the terms surface tension and capillarity.

Calculate the dynamic viscosity of an oil, which is used for lubrication between a square plate of size $ 0.8 \, m \times 0.8 $ m and an inclined plane with angle of inclination $ 30^{\circ} $. The weight of the square plate is 300 N and its slides down the inclined plane with a uniform velocity of $ 0.3 \, m/s $. The thickness of oil film is 1.5 mm.

Differentiate between simple manometer and differential manometer.

State the Pascal's law.

A U-tube differential manometer connects two pressure pipes A and B. Pipe A contains carbon tetrachloride having a specific gravity 1.594 under a pressure of 11.772 $ N/cm^2 $ and pipe B contains oil of sp. gr. 0.8 under a pressure of 11.772 $ N/cm^2 $. The pipe A lies 2.5 m above pipe B. Find the difference of pressure measured by mercury as fluid filling U-tube.

Derive an expression for the depth of centre of pressure from free surface of liquid of an inclined plane surface submerged in the liquid.

A solid cylinder of diameter 4.0 m has a height of 3 meters. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder = 0.6.

Define the terms (i) streamline, (ii) unsteady flow and (iii) laminar and turbulent flow.

What do you understand by flow nets?

The velocity vector in a fluid flow is given by $ V = 4x^3i - 10x^2yj + 2tk $. Find the velocity and acceleration of a fluid particle at (2, 1, 3) at a time $ t = 1 $.

Derive an expression for Bernoulli's theorem from first principle and state the assumptions made for such a derivation.

The water is flowing through a pipe having diameters 20 cm and 10 cm at inlet and outlet respectively. The rate of flow through pipe is 35 litres/s. The inlet is 6 m above datum and outlet is 4 m above datum. If the pressure at inlet is 39.24 $ N/cm^2 $, find the intensity of pressure at outlet.

Discuss the relative merits and demerits of venturi meter with respect to orifice meter.

Prove that the discharge through venturi meter by the relation $ Q_{act} = C_d \frac{a_1 a_2}{\sqrt{a_1^2 - a_2^2}} \sqrt{2gh} $ where, $ a_1 $ = area of pipe at inlet, $ a_2 $ = area at throat.

What do you understand by the terms 'major energy loss' and 'minor energy loss' in pipes?

With the help of a suitable diagram, explain hydraulic gradient line and total energy line.

SAE 10 oil is flowing through a pipeline at a velocity of $ 1.0 \, m/s $. The pipe is 45 m long and has a diameter of 150 mm. Find the head loss due to friction. [$ \rho = 869 \, kg/m^3 $ and $ \mu = 0.0814 \, kg/m-s $]

Define Reynolds number. Water is flowing through a pipe of diameter 30 cm at a velocity of 4 m/s. Find the velocity of oil flowing in another pipe of diameter 10 cm, if the condition of dynamic similarity is satisfied between the two pipes. The viscosity of water and oil is given as 0.01 poise and 0.025 poise. The sp. gr. of oil = 0.8.

Differentiate between streamline body and bluff body. With the help of a suitable diagram, show the different regimes of boundary layer separation for flow over a cylinder.

Consider the following relationship between the shear stress and the rate of shear strain $ \tau = \mu \left(\frac{du}{dy}\right)^n $. When the exponent n is greater than 1, the fluid is known as

What is the pressure difference between inside and outside of a droplet of water?

A floating body has centre of buoyancy at B, centre of gravity at G and metacentre at M. Then for stable equilibrium of the body

At the point of boundary layer separation

If x is the distance from the leading edge of a plate, then thickness of laminar boundary layer varies as

The velocity profile of a fully developed laminar flow in a straight circular pipe is given by the expression $ u(r) = -\frac{R^2}{4\mu} \left(\frac{dp}{dx}\right) \left[1 - \frac{r^2}{R^2}\right] $ where $ \frac{dp}{dx} $ is constant and the symbols have their usual meanings. The average velocity of fluid in the pipe is

A jet of water impinges with velocity v on a plate which is inclined at angle $ \alpha $ with the direction of jet. The force exerted on the plate in a direction normal to flow is

A vessel contains oil (density 0.8 $ g/cm^3 $) over mercury (density 13.6 $ g/cm^3 $). A homogeneous sphere floats with half its volume immersed in mercury and the other half is in oil. The density of the material of the sphere in $ g/cm^3 $ is

Euler's dimensionless number relates

What is the dimension of kinematic viscosity of a fluid?

State the Newton's law of viscosity. Explain the effect of temperature on viscosity of water and that of air.

Define the terms surface tension and capillarity.

Calculate the dynamic viscosity of an oil, which is used for lubrication between a square plate of size $ 0.8 \, m \times 0.8 $ m and an inclined plane with angle of inclination $ 30^{\circ} $. The weight of the square plate is 300 N and its slides down the inclined plane with a uniform velocity of $ 0.3 \, m/s $. The thickness of oil film is 1.5 mm.

Differentiate between simple manometer and differential manometer.

State the Pascal's law.

A U-tube differential manometer connects two pressure pipes A and B. Pipe A contains carbon tetrachloride having a specific gravity 1.594 under a pressure of 11.772 $ N/cm^2 $ and pipe B contains oil of sp. gr. 0.8 under a pressure of 11.772 $ N/cm^2 $. The pipe A lies 2.5 m above pipe B. Find the difference of pressure measured by mercury as fluid filling U-tube.

Derive an expression for the depth of centre of pressure from free surface of liquid of an inclined plane surface submerged in the liquid.

A solid cylinder of diameter 4.0 m has a height of 3 meters. Find the meta-centric height of the cylinder when it is floating in water with its axis vertical. The sp. gr. of the cylinder = 0.6.

Define the terms (i) streamline, (ii) unsteady flow and (iii) laminar and turbulent flow.

What do you understand by flow nets?

The velocity vector in a fluid flow is given by $ V = 4x^3i - 10x^2yj + 2tk $. Find the velocity and acceleration of a fluid particle at (2, 1, 3) at a time $ t = 1 $.

Derive an expression for Bernoulli's theorem from first principle and state the assumptions made for such a derivation.

The water is flowing through a pipe having diameters 20 cm and 10 cm at inlet and outlet respectively. The rate of flow through pipe is 35 litres/s. The inlet is 6 m above datum and outlet is 4 m above datum. If the pressure at inlet is 39.24 $ N/cm^2 $, find the intensity of pressure at outlet.

Discuss the relative merits and demerits of venturi meter with respect to orifice meter.

Prove that the discharge through venturi meter by the relation $ Q_{act} = C_d \frac{a_1 a_2}{\sqrt{a_1^2 - a_2^2}} \sqrt{2gh} $ where, $ a_1 $ = area of pipe at inlet, $ a_2 $ = area at throat.

What do you understand by the terms 'major energy loss' and 'minor energy loss' in pipes?

With the help of a suitable diagram, explain hydraulic gradient line and total energy line.

SAE 10 oil is flowing through a pipeline at a velocity of $ 1.0 \, m/s $. The pipe is 45 m long and has a diameter of 150 mm. Find the head loss due to friction. [$ \rho = 869 \, kg/m^3 $ and $ \mu = 0.0814 \, kg/m-s $]

Define Reynolds number. Water is flowing through a pipe of diameter 30 cm at a velocity of 4 m/s. Find the velocity of oil flowing in another pipe of diameter 10 cm, if the condition of dynamic similarity is satisfied between the two pipes. The viscosity of water and oil is given as 0.01 poise and 0.025 poise. The sp. gr. of oil = 0.8.

Differentiate between streamline body and bluff body. With the help of a suitable diagram, show the different regimes of boundary layer separation for flow over a cylinder.

The resultant hydrostatic force acts through a point is known as

For a floating body, the buoyant force passes through the

The streamline is a line

An orifice is known as large orifice when the head of liquid from the centre of the orifice is

Bernoulli's theorem deals with the law of conservation of

Irrotational flow means

The coefficient of friction of laminar flow through a circular pipe is given by

Models are known undistorted model, if

The geometric similarity between model and prototype means

Poise is the unit of

Define the terms 'buoyancy' and 'centre of buoyancy'. Derive an expression for the metacentric height of a floating body.

Find the volume of the water displaced and position of centre of buoyancy for a wooden block of width 2.5 m and of depth 1.5 m when it floats horizontally in water. The density of wooden block is $ 650~kg/m^3 $ and its length is 6.0 m.

The velocity components for a steady flow are given as $ u=0 $, $ v=-y^3-4z $, $ w=3y^2z $. Determine (i) whether the flow field is one-, two- or three-dimensional, (ii) whether the flow is compressible and (iii) the stream function for the flow.

Show that the equation of continuity reduces to Laplace's equation when the liquid is incompressible and irrotational.

A plate, 0.025 mm distance from a fixed plate, moves at $ 60~cm/s $ and requires a force of 2 newton per unit area, i.e., $ 2~N/m^2 $ to maintain this speed. Determine the fluid viscosity between the plates.

A pipe branches into two pipes as shown in Fig. 1 below: The pipe has diameter of 55 cm at A, 25 cm at B, 28 cm at C and 17 cm at D. If the velocity at A and C be $ 2~m/sec $ and $ 4~m/sec $ respectively, then find the total quantity of liquid at A and velocities at B and D.

State Bernoulli's theorem for steady flow of an incompressible fluid. Derive an expression for Bernoulli's equation from first principle and state the assumption made for such a derivation.

Water is flowing through a pipe of 5 cm diameter under a pressure of $ 29\cdot43~N/cm^2 $ (gauge) and with mean velocity of $ 2\cdot0~m/s $. Find the total head or total energy per unit weight of the water at cross section, which is 5 m above the datum line.

Discuss the relative merits and demerits of venturimeter with respect to orifice-meter.

What is a pitot tube? How will you determine the velocity at any point with the help of pitot tube?

Discuss the Hardy cross method for pipe network.

Calculate the discharge in each pipe of the network shown in the Fig. 2 given below. The pipe network consists of 5 pipes. The head loss $ h_f $ in pipe is given by $ h_f=rQ^2 $. The values of r for various pipes and also the inflow or outflows at nodes are shown in the Fig. 2 below.

Define laminar flow. Discuss generalized plane Couette flow between parallel plates. Determine the volumetric flow rate, shear stress and coefficient of friction.

Oil flows between two parallel plates, one of which is at rest and the other moves with a velocity U. If the pressure is decreasing in the direction of the flow at a rate of $ 0\cdot10~lbf/ft^3 $, the dynamic viscosity is $ 10^{-3}lbf-sec/ft^2 $, the spacing of the plates is 2 inches and volumetric flow Q per unit width is $ 0.15~ft^2/sec $, what is the value of U?

Discuss types of similarity and explain each of them.

Using Buckingham's $ \pi $ theorem, show that the frictional torque T of a disk of diameter D rotating at a speed N in a fluid of viscosity $ \mu $, density $ \rho $ in a turbulent flow is given by $ T=D^5N^2\rho\phi\left(\frac{\mu}{D^2N\rho}\right) $

The resultant hydrostatic force acts through a point is known as

For a floating body, the buoyant force passes through the

The streamline is a line

An orifice is known as large orifice when the head of liquid from the centre of the orifice is

Bernoulli's theorem deals with the law of conservation of

Irrotational flow means

The coefficient of friction of laminar flow through a circular pipe is given by

Models are known undistorted model, if

The geometric similarity between model and prototype means

Poise is the unit of

Define the terms 'buoyancy' and 'centre of buoyancy'. Derive an expression for the metacentric height of a floating body.

Find the volume of the water displaced and position of centre of buoyancy for a wooden block of width 2.5 m and of depth 1.5 m when it floats horizontally in water. The density of wooden block is $ 650~kg/m^3 $ and its length is 6.0 m.

The velocity components for a steady flow are given as $ u=0 $, $ v=-y^3-4z $, $ w=3y^2z $. Determine (i) whether the flow field is one-, two- or three-dimensional, (ii) whether the flow is compressible and (iii) the stream function for the flow.

Show that the equation of continuity reduces to Laplace's equation when the liquid is incompressible and irrotational.

A plate, 0.025 mm distance from a fixed plate, moves at $ 60~cm/s $ and requires a force of 2 newton per unit area, i.e., $ 2~N/m^2 $ to maintain this speed. Determine the fluid viscosity between the plates.

A pipe branches into two pipes as shown in Fig. 1 below: The pipe has diameter of 55 cm at A, 25 cm at B, 28 cm at C and 17 cm at D. If the velocity at A and C be $ 2~m/sec $ and $ 4~m/sec $ respectively, then find the total quantity of liquid at A and velocities at B and D.

State Bernoulli's theorem for steady flow of an incompressible fluid. Derive an expression for Bernoulli's equation from first principle and state the assumption made for such a derivation.

Water is flowing through a pipe of 5 cm diameter under a pressure of $ 29\cdot43~N/cm^2 $ (gauge) and with mean velocity of $ 2\cdot0~m/s $. Find the total head or total energy per unit weight of the water at cross section, which is 5 m above the datum line.

Discuss the relative merits and demerits of venturimeter with respect to orifice-meter.

What is a pitot tube? How will you determine the velocity at any point with the help of pitot tube?

Discuss the Hardy cross method for pipe network.

Calculate the discharge in each pipe of the network shown in the Fig. 2 given below. The pipe network consists of 5 pipes. The head loss $ h_f $ in pipe is given by $ h_f=rQ^2 $. The values of r for various pipes and also the inflow or outflows at nodes are shown in the Fig. 2 below.

Define laminar flow. Discuss generalized plane Couette flow between parallel plates. Determine the volumetric flow rate, shear stress and coefficient of friction.

Oil flows between two parallel plates, one of which is at rest and the other moves with a velocity U. If the pressure is decreasing in the direction of the flow at a rate of $ 0\cdot10~lbf/ft^3 $, the dynamic viscosity is $ 10^{-3}lbf-sec/ft^2 $, the spacing of the plates is 2 inches and volumetric flow Q per unit width is $ 0.15~ft^2/sec $, what is the value of U?

Discuss types of similarity and explain each of them.

Using Buckingham's $ \pi $ theorem, show that the frictional torque T of a disk of diameter D rotating at a speed N in a fluid of viscosity $ \mu $, density $ \rho $ in a turbulent flow is given by $ T=D^5N^2\rho\phi\left(\frac{\mu}{D^2N\rho}\right) $

Discharge coefficient of a 'Venturimeter' is:

Correct unit for Kinematic Viscosity is:

For 2-D flow field, the equation of streamline is given as:

The stream function for a 2-D flow is given by $ \psi=2xy+ $ constant. The flow between the streamlines (1,1) and (2,2) would be:

Consider the Chezy's equation for the flow velocity through a channel: $ V=C\sqrt{mi} $ where V is flow velocity in m/s, m is the hydraulic mean depth in meter and i is longitudinal slope of the channel. The dimensions of the Chezy constant C are:

Each term of Bernoulli' equation has the unit of:

The equation of motion for a viscous fluid are known as:

Momentum integral equation for zero pressure gradient is given by:

The pressure at the bottom of a water Lake is 1.5 times to that at half the depth. If the water barometer reads 10 m, the depth of lake is:

The Bernoulli equation refers to the conservation of:

State the Newton's law of viscosity and give examples of its application.

The velocity distribution for flow over a flat plate is given by $ u=\frac{3}{4}y-y^2 $ in which u is the velocity in meter per second at a distance y metre above the plate. Determine the shear stress at $ y=0.15m $. Take dynamic viscosity of fluid as 8.6 poise.

An inclined-tube reservoir manometer is constructed as shown in Fig. 1. Derive a general expression for the liquid deflection, L, in the inclined tube, due to the applied pressure difference, $ \Delta p $. Also obtain an expression for the manometer sensitivity, and discuss the effect on sensitivity of D, d, $ \theta $ and SG.

What is manometer? How are they classified?

Derive an expression for the depth of centre of pressure from free surface of liquid of an inclined plate surface submerged in the liquid.

Determine the total pressure on a circular plate of diameter 1.5 m which is placed vertically in water in such a way that the centre of the plate is 3 m below the free surface of water. Find the position of centre of pressure.

Consider a flow with velocity components $ u=0 $, $ v=-y^3-4z $, and $ w=3y^2z $. i. Is this a one-, two-, or three-dimensional flow? ii. Demonstrate whether this is an incompressible or compressible flow. iii. Derive a stream function for this flow.

What do you understand by 'local acceleration' and 'convective acceleration'?

A 300 mm diameter pipe carries water under a head of 20 m with a velocity of $ 3.5~m/s $. If the axis of the pipe turns through $ 45^{\circ} $ find the magnitude and direction of the resultant force at the bend.

What is venturimeter? Derive an expression for the discharge through a venturimeter.

When tested in water ($ \rho=998kg/m^3 $ and $ \mu=0.001~kg/m.s $) flowing at $ 2~m/s $, an 8 cm diameter sphere has a measured drag of 5 N. What will be the velocity and drag force on a 1.5 m diameter weather balloon moored in sea-level standard air ($ \rho=1.2255~kg/m^3 $ and $ \mu=1.78\times10^{-5}kg/m.s $)?

The drag force, F, on a smooth sphere depends on the relative velocity, V, the sphere diameter, D, the fluid density, $ \rho $, and the fluid viscosity, $ \mu $. Obtain a set of dimensionless groups that can be used to correlate experimental data.

In Fig.2 the flowing fluid is $ CO_2 $ at $ 20^{\circ}C $. Neglect losses. If $ P_1=170~kPa $ and the manometer fluid is Meriam red oil (SG=0.827), estimate (a) $ p_2 $ and (b) the gas flow rate in $ m^3/h $.

What do you mean by boundary layer separation? Discuss the methods of preventing the separation of boundary layer.

Write short notes on following: (i) Navier-Stokes Equation (ii) Flow Net (iii) Friction Drag and Pressure drag

Discharge coefficient of a 'Venturimeter' is:

Correct unit for Kinematic Viscosity is:

For 2-D flow field, the equation of streamline is given as:

The stream function for a 2-D flow is given by $ \psi=2xy+ $ constant. The flow between the streamlines (1,1) and (2,2) would be:

Consider the Chezy's equation for the flow velocity through a channel: $ V=C\sqrt{mi} $ where V is flow velocity in m/s, m is the hydraulic mean depth in meter and i is longitudinal slope of the channel. The dimensions of the Chezy constant C are:

Each term of Bernoulli' equation has the unit of:

The equation of motion for a viscous fluid are known as:

Momentum integral equation for zero pressure gradient is given by:

The pressure at the bottom of a water Lake is 1.5 times to that at half the depth. If the water barometer reads 10 m, the depth of lake is:

The Bernoulli equation refers to the conservation of:

State the Newton's law of viscosity and give examples of its application.

The velocity distribution for flow over a flat plate is given by $ u=\frac{3}{4}y-y^2 $ in which u is the velocity in meter per second at a distance y metre above the plate. Determine the shear stress at $ y=0.15m $. Take dynamic viscosity of fluid as 8.6 poise.

An inclined-tube reservoir manometer is constructed as shown in Fig. 1. Derive a general expression for the liquid deflection, L, in the inclined tube, due to the applied pressure difference, $ \Delta p $. Also obtain an expression for the manometer sensitivity, and discuss the effect on sensitivity of D, d, $ \theta $ and SG.

What is manometer? How are they classified?

Derive an expression for the depth of centre of pressure from free surface of liquid of an inclined plate surface submerged in the liquid.

Determine the total pressure on a circular plate of diameter 1.5 m which is placed vertically in water in such a way that the centre of the plate is 3 m below the free surface of water. Find the position of centre of pressure.

Consider a flow with velocity components $ u=0 $, $ v=-y^3-4z $, and $ w=3y^2z $. i. Is this a one-, two-, or three-dimensional flow? ii. Demonstrate whether this is an incompressible or compressible flow. iii. Derive a stream function for this flow.

What do you understand by 'local acceleration' and 'convective acceleration'?

A 300 mm diameter pipe carries water under a head of 20 m with a velocity of $ 3.5~m/s $. If the axis of the pipe turns through $ 45^{\circ} $ find the magnitude and direction of the resultant force at the bend.

What is venturimeter? Derive an expression for the discharge through a venturimeter.

When tested in water ($ \rho=998kg/m^3 $ and $ \mu=0.001~kg/m.s $) flowing at $ 2~m/s $, an 8 cm diameter sphere has a measured drag of 5 N. What will be the velocity and drag force on a 1.5 m diameter weather balloon moored in sea-level standard air ($ \rho=1.2255~kg/m^3 $ and $ \mu=1.78\times10^{-5}kg/m.s $)?

The drag force, F, on a smooth sphere depends on the relative velocity, V, the sphere diameter, D, the fluid density, $ \rho $, and the fluid viscosity, $ \mu $. Obtain a set of dimensionless groups that can be used to correlate experimental data.

In Fig.2 the flowing fluid is $ CO_2 $ at $ 20^{\circ}C $. Neglect losses. If $ P_1=170~kPa $ and the manometer fluid is Meriam red oil (SG=0.827), estimate (a) $ p_2 $ and (b) the gas flow rate in $ m^3/h $.

What do you mean by boundary layer separation? Discuss the methods of preventing the separation of boundary layer.

Write short notes on following: (i) Navier-Stokes Equation (ii) Flow Net (iii) Friction Drag and Pressure drag

An ideal fluid

Typical example of a non-Newtonian fluid of pseudoplastic variety is

If G is the centre of gravity, B is centre of buoyancy and M is metacentre of a floating body, then for the body to be in unstable equilibrium, when

The centre of buoyancy is

The continuity equation represents the conservation of

A steady irrotational flow of an incompressible fluid is called

Each term of Bernoulli's equation stated in the form $ \frac{p}{w}+\frac{V^2}{2g}+y = \text{constant} $, has unit of

Euler's dimensionless number relates

The lift force, per unit length, on a cylinder depends on

The equations of motion for a viscous fluid are known as

Explain the classification of fluids based on Newton's law of viscosity. Give the examples also.

The velocity distribution in a pipeline is prescribed by the relation $ u=2y-y^2 $, where u denotes the velocity at a distance y from the solid boundary. Calculate- (i) shear stress at the wall; (ii) shear stress at 0.5 cm from the wall; (iii) total resistance for a 2 cm diameter pipe over a length of 100 m. Assume coefficient of viscosity $ \mu=0.4 $ poise.

A rectangular burge of width b and a submerged depth of H has its centre of gravity at the waterline. Find the metacentric height in terms of b/H and hence show that for stable equilibrium of the burge $ b/H\ge\sqrt{6} $.

Define surface tension. Prove that the relationship between surface tension and pressure inside a droplet of liquid in excess of outside pressure is given by $ P=\frac{4\sigma}{d} $

Define pressure. Obtain an expression for the pressure intensity at a point in a fluid.

The figure shows an inverted differential manometer which is connected to two pipes A and B which convey water. The fluid in manometer is oil of specific gravity 0.8. For the manometer readings shown in the figure, find the pressure difference between A and B.

Define the equation of continuity. Obtain an expression for continuity equation for a three-dimensional flow.

A fluid flow field is given by $ V=x^2yi+y^2zj-(2xyz+yz^2)k $. Prove that it is a possible steady incompressible fluid flow. Calculate the velocity and acceleration at the point (2, 1, 3).

In a 100 mm diameter horizontal pipe and a venturimeter of 0.5 contraction ratio has been fixed. The head of water on the meter when there is no flow is 3 m (gauge). Find the rate of flow for which the throat pressure will be 2 meters of water absolute. The coefficient of discharge is 0.97. Take atmospheric pressure head = 10.3 m of water.

(i) What are the assumptions made in the derivation of Bernoulli's equation? (ii) Write down Bernoulli's equation and explain the different terms.

State Buckingham's $ \pi $ theorem. Show that the resistance R to the motion of a sphere of diameter D moving with a uniform velocity V through a real fluid having mass density $ \rho $ and viscosity $ \mu $ is given by $ R=\rho D^2V^2f\left(\frac{\mu}{\rho VD}\right) $.

Explain the Rayleigh's method for dimensional analysis.

An airfoil of chord length 2 m and of span 15 m has an angle of attack as $ 16^{\circ} $. The airfoil is moving with a velocity of $ 80~m/sec $ in air whose density is $ 1.25~kg/m^3 $. Find the weight of the airfoil and the power required to drive it. The values of coefficient of drag and lift corresponding to angle of attack are given as 0.03 and 0.5 respectively.

Define the following terms: (i) Drag (ii) Lift

Write short notes on any three of the following: (a) Boundary layer separation and its control (b) Pitot tube (c) Hydraulic Grade Line (HGL) (d) Circulation and vorticity (e) Different types of fluid motion

An ideal fluid

Typical example of a non-Newtonian fluid of pseudoplastic variety is

If G is the centre of gravity, B is centre of buoyancy and M is metacentre of a floating body, then for the body to be in unstable equilibrium, when

The centre of buoyancy is

The continuity equation represents the conservation of

A steady irrotational flow of an incompressible fluid is called

Each term of Bernoulli's equation stated in the form $ \frac{p}{w}+\frac{V^2}{2g}+y = \text{constant} $, has unit of

Euler's dimensionless number relates

The lift force, per unit length, on a cylinder depends on

The equations of motion for a viscous fluid are known as

Explain the classification of fluids based on Newton's law of viscosity. Give the examples also.

The velocity distribution in a pipeline is prescribed by the relation $ u=2y-y^2 $, where u denotes the velocity at a distance y from the solid boundary. Calculate- (i) shear stress at the wall; (ii) shear stress at 0.5 cm from the wall; (iii) total resistance for a 2 cm diameter pipe over a length of 100 m. Assume coefficient of viscosity $ \mu=0.4 $ poise.

A rectangular burge of width b and a submerged depth of H has its centre of gravity at the waterline. Find the metacentric height in terms of b/H and hence show that for stable equilibrium of the burge $ b/H\ge\sqrt{6} $.

Define surface tension. Prove that the relationship between surface tension and pressure inside a droplet of liquid in excess of outside pressure is given by $ P=\frac{4\sigma}{d} $

Define pressure. Obtain an expression for the pressure intensity at a point in a fluid.

The figure shows an inverted differential manometer which is connected to two pipes A and B which convey water. The fluid in manometer is oil of specific gravity 0.8. For the manometer readings shown in the figure, find the pressure difference between A and B.

Define the equation of continuity. Obtain an expression for continuity equation for a three-dimensional flow.

A fluid flow field is given by $ V=x^2yi+y^2zj-(2xyz+yz^2)k $. Prove that it is a possible steady incompressible fluid flow. Calculate the velocity and acceleration at the point (2, 1, 3).

In a 100 mm diameter horizontal pipe and a venturimeter of 0.5 contraction ratio has been fixed. The head of water on the meter when there is no flow is 3 m (gauge). Find the rate of flow for which the throat pressure will be 2 meters of water absolute. The coefficient of discharge is 0.97. Take atmospheric pressure head = 10.3 m of water.

(i) What are the assumptions made in the derivation of Bernoulli's equation? (ii) Write down Bernoulli's equation and explain the different terms.

State Buckingham's $ \pi $ theorem. Show that the resistance R to the motion of a sphere of diameter D moving with a uniform velocity V through a real fluid having mass density $ \rho $ and viscosity $ \mu $ is given by $ R=\rho D^2V^2f\left(\frac{\mu}{\rho VD}\right) $.

Explain the Rayleigh's method for dimensional analysis.

An airfoil of chord length 2 m and of span 15 m has an angle of attack as $ 16^{\circ} $. The airfoil is moving with a velocity of $ 80~m/sec $ in air whose density is $ 1.25~kg/m^3 $. Find the weight of the airfoil and the power required to drive it. The values of coefficient of drag and lift corresponding to angle of attack are given as 0.03 and 0.5 respectively.

Define the following terms: (i) Drag (ii) Lift

Write short notes on any three of the following: (a) Boundary layer separation and its control (b) Pitot tube (c) Hydraulic Grade Line (HGL) (d) Circulation and vorticity (e) Different types of fluid motion

Falling drops of water become spherical due to

The coefficient of viscosity is a property of

The continuity equation represents conservation of

A streamline is a line

Navier-Stokes equations are associated with

The velocity distribution at any section of a pipe for steady laminar flow is

Which of the following has the form of Reynolds number?

The square root of inertia force to gravity force is known as

One atmospheric pressure equals

The range of coefficient of discharge for a venturimeter is

Check whether the following functions represent possible flow phenomenon of irrotational type: (i) $ \phi=x^2-y^2+y $ (ii) $ \phi=\sin(x+y+z) $ (iii) $ \phi=\frac{4x}{x^2+y^2} $

Define surface tension. Prove that the relationship between surface tension and pressure inside a droplet of liquid in excess of outside pressure is given by $ P=\frac{4\sigma}{d} $

With neat sketches, explain the conditions of equilibrium for floating and submerged bodies.

A differential manometer is connected at the two points A and B as shown in the figure below: At B, air pressure is $ 9\cdot81~N/cm^2 $ (absolute), find the absolute pressure at A.

Derive Euler's equation of motion along a streamline and hence derive the Bernoulli's theorem.

A conical tube 1.5 m long is fixed vertically with its smaller end upwards and it forms a part of pipeline. Water flows down the tube and measurements indicate that velocity is $ 4.5~m/sec $ at the smaller end, $ 1.5~m/sec $ at the larger end and the pressure head is 10 m of water at the upper end. Presuming that loss of head in the tube is expressed as $ \frac{0\cdot33(v_1-v_2)^2}{2g} $ where $ v_1 $ and $ v_2 $ are the velocities at the upper and lower ends, make calculations for the pressure head at the lower end of the conical tube.

The details of a parallel-pipe system for water flow are shown in the figure below: (i) If the frictional drop between the junctions is 15 m of water, determine the total flow rate. (ii) If the total flow rate is $ 0\cdot66~m^3/sec $, determine the individual flow and the friction drop.

Find the difference in drag force exerted on a flat plate of size $ 2~m\times2~m $ when the plate is moving at a speed of $ 4~m/sec $ normal to its plane in (i) water and (ii) air of density $ 1\cdot24~kg/m^3 $. Coefficient of drag is given as 1.15.

Prove that the discharge through a triangular notch or weir is given by $ Q=\frac{8}{15}C_d\tan(\theta/2)\sqrt{2g}H^{5/2} $

The head of water over a rectangular notch is 900 mm. The discharge is $ 300~litres/sec $. Find the length of the notch, when $ C_d=0.62 $.

Using Rayleigh's method, determine the rational formula for discharge Q through a sharp-edged orifice freely into the atmosphere in terms of constant head H, diameter d, mass density $ \rho $, dynamic viscosity $ \mu $ and acceleration due to gravity g.

Define the following:
(i) Laminar and turbulent flow
(ii) Rotational and irrotational flow
(iii) Uniform and non-uniform flow./p>

Define the equation of continuity. Obtain an expression for continuity equation for a three-dimensional flow.

(i) What do you mean by equipotential line and a line of constant stream function? (ii) Describe the uses and limitations of the flow nets.

Write short notes on any three of the following: (a) Boundary layer separation and its control (b) Different types of fluid (c) Hydraulic Grade Line (HGL) (d) Pitot tube (e) Circulation and vorticity

Falling drops of water become spherical due to

The coefficient of viscosity is a property of

The continuity equation represents conservation of

A streamline is a line

Navier-Stokes equations are associated with

The velocity distribution at any section of a pipe for steady laminar flow is

Which of the following has the form of Reynolds number?

The square root of inertia force to gravity force is known as

One atmospheric pressure equals

The range of coefficient of discharge for a venturimeter is

Check whether the following functions represent possible flow phenomenon of irrotational type: (i) $ \phi=x^2-y^2+y $ (ii) $ \phi=\sin(x+y+z) $ (iii) $ \phi=\frac{4x}{x^2+y^2} $

Define surface tension. Prove that the relationship between surface tension and pressure inside a droplet of liquid in excess of outside pressure is given by $ P=\frac{4\sigma}{d} $

With neat sketches, explain the conditions of equilibrium for floating and submerged bodies.

A differential manometer is connected at the two points A and B as shown in the figure below: At B, air pressure is $ 9\cdot81~N/cm^2 $ (absolute), find the absolute pressure at A.

Derive Euler's equation of motion along a streamline and hence derive the Bernoulli's theorem.

A conical tube 1.5 m long is fixed vertically with its smaller end upwards and it forms a part of pipeline. Water flows down the tube and measurements indicate that velocity is $ 4.5~m/sec $ at the smaller end, $ 1.5~m/sec $ at the larger end and the pressure head is 10 m of water at the upper end. Presuming that loss of head in the tube is expressed as $ \frac{0\cdot33(v_1-v_2)^2}{2g} $ where $ v_1 $ and $ v_2 $ are the velocities at the upper and lower ends, make calculations for the pressure head at the lower end of the conical tube.

The details of a parallel-pipe system for water flow are shown in the figure below: (i) If the frictional drop between the junctions is 15 m of water, determine the total flow rate. (ii) If the total flow rate is $ 0\cdot66~m^3/sec $, determine the individual flow and the friction drop.

Find the difference in drag force exerted on a flat plate of size $ 2~m\times2~m $ when the plate is moving at a speed of $ 4~m/sec $ normal to its plane in (i) water and (ii) air of density $ 1\cdot24~kg/m^3 $. Coefficient of drag is given as 1.15.

Prove that the discharge through a triangular notch or weir is given by $ Q=\frac{8}{15}C_d\tan(\theta/2)\sqrt{2g}H^{5/2} $

The head of water over a rectangular notch is 900 mm. The discharge is $ 300~litres/sec $. Find the length of the notch, when $ C_d=0.62 $.

Using Rayleigh's method, determine the rational formula for discharge Q through a sharp-edged orifice freely into the atmosphere in terms of constant head H, diameter d, mass density $ \rho $, dynamic viscosity $ \mu $ and acceleration due to gravity g.

Define the following:
(i) Laminar and turbulent flow
(ii) Rotational and irrotational flow
(iii) Uniform and non-uniform flow./p>

Define the equation of continuity. Obtain an expression for continuity equation for a three-dimensional flow.

(i) What do you mean by equipotential line and a line of constant stream function? (ii) Describe the uses and limitations of the flow nets.

Write short notes on any three of the following: (a) Boundary layer separation and its control (b) Different types of fluid (c) Hydraulic Grade Line (HGL) (d) Pitot tube (e) Circulation and vorticity

Answer any seven questions from the following is short, preferably 1 or 2 sentence(s). What are the following?

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Write short notes on any three of the following:

Write short notes on any seven of the following, preferably one or two sentence(s):

Answer the following:

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Write short notes on any three of the following: