Introduction to Fluid Mechanics

Surface tension is due to

An oil of specific gravity 0.9 has viscosity of 0.28 stokes at $ 38^{\circ}C $. What will be its viscosity in $ Ns/m^2 $?

Which property of mercury is the main reason for its use in barometers?

The centre of pressure for an inclined surface area

The buoyancy force is

The flow in pipe whose valve is being opened or closed gradually is an example of

Which one of the following is measured by a rotameter?

In flow through a pipe, the transition from laminar to turbulent flow does not depend on

The laminar flow is characterized by Reynolds number which is

Kinematic similarity between model and prototype is the similarity of

Define the following fluid Properties: (i) Weight density (ii) Specific volume (iii) Specific gravity (iv) Viscosity.

Two large plane surfaces are 3.0 cm apart. The space between the surfaces is filled with glycerine. What force is required to drag a very thin plate of surface area $ 1.0 \, m^2 $ between the two large plane surface at a speed of $ 0.75 \, m/sec $ if the thin plate is at a distance of 1.0 cm from one of the plane surfaces? Assume dynamic viscosity of glycerine as $ 8.10 \times 10^{-1} \, N-s/m^2 $.

Derive an expression for the meta-centric height of a floating body.

A vertical sluice gate is used to cover an opening in a dam. The opening is 2 m wide and 1.2 m high. On the upstream of the gate, the liquid of sp.gr. 1.45, lies upto a height of 1.5 m above the top of the gate, whereas on the downstream side the water is available upto a height touching the top of the gate. Find the resultant force acting on the gate and position of centre of pressure. Find also the force acting horizontally at the top of the gate which is capable of opening it. Assume that the gate is hinged at the bottom.

Define and distinguish between streamline, path line and streak line.

A 40 cm diameter pipe, conveying water, branches into two pipes of diameters 30 cm and 20 cm respectively. If the average velocity in the 40 cm diameter pipe is $ 3 \, m/s $. Find the discharge in this pipe. Also determine the velocity in 20 cm pipe if the average velocity in 30 cm diameter pipe is $ 2 \, m/s $.

Derive Bernoulli's equation for the flow of an incompressible frictionless fluid from consideration of momentum.

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

Derive an expression for loss of head due to friction in pipes.

A pipe, 100 mm in diameter, has a nozzle attached to it at the discharge end, the diameter of the nozzle is 50 mm. The rate of discharge of water through the nozzle is $ 20 \, litres/s $ and the pressure at the base of the nozzle of $ 5.886 \, N/cm^2 $. Calculate the co-efficient of discharge. Assume that the base of the nozzle and outlet of the nozzle are at the same elevation.

A smooth pipe of diameter 400 mm and length 800 m carries water at the rate of $ 0.04 \, m^3/s $. Determine the head lost due to friction, wall shear stress, centre-line velocity and thickness of laminar sub-layer. Take the kinematic viscosity of water as 0.018 stokes.

Distinguish between: (i) Steady flow and un-steady flow (ii) Uniform and non-uniform flow (iii) Compressible and incompressible flow (iv) Rotational and irrotational flow.

Explain the significance of non-dimensional number: (i) Reynolds number (ii) Froude number (iii) Mach number (iv) Weber number.

A wooden block (of specific gravity 0.70) of size $ 150 \times 15 \times 30 $ cm floats horizontally on the surface of sea water (specific weight $ 1025 \, kg/m^3 $). Calculate the volume of water displaced, depth of immersion and the position of centre of buoyancy. Also find the metacentric height of the block.

Surface tension is due to

An oil of specific gravity 0.9 has viscosity of 0.28 stokes at $ 38^{\circ}C $. What will be its viscosity in $ Ns/m^2 $?

Which property of mercury is the main reason for its use in barometers?

The centre of pressure for an inclined surface area

The buoyancy force is

The flow in pipe whose valve is being opened or closed gradually is an example of

Which one of the following is measured by a rotameter?

In flow through a pipe, the transition from laminar to turbulent flow does not depend on

The laminar flow is characterized by Reynolds number which is

Kinematic similarity between model and prototype is the similarity of

Define the following fluid Properties: (i) Weight density (ii) Specific volume (iii) Specific gravity (iv) Viscosity.

Two large plane surfaces are 3.0 cm apart. The space between the surfaces is filled with glycerine. What force is required to drag a very thin plate of surface area $ 1.0 \, m^2 $ between the two large plane surface at a speed of $ 0.75 \, m/sec $ if the thin plate is at a distance of 1.0 cm from one of the plane surfaces? Assume dynamic viscosity of glycerine as $ 8.10 \times 10^{-1} \, N-s/m^2 $.

Derive an expression for the meta-centric height of a floating body.

A vertical sluice gate is used to cover an opening in a dam. The opening is 2 m wide and 1.2 m high. On the upstream of the gate, the liquid of sp.gr. 1.45, lies upto a height of 1.5 m above the top of the gate, whereas on the downstream side the water is available upto a height touching the top of the gate. Find the resultant force acting on the gate and position of centre of pressure. Find also the force acting horizontally at the top of the gate which is capable of opening it. Assume that the gate is hinged at the bottom.

Define and distinguish between streamline, path line and streak line.

A 40 cm diameter pipe, conveying water, branches into two pipes of diameters 30 cm and 20 cm respectively. If the average velocity in the 40 cm diameter pipe is $ 3 \, m/s $. Find the discharge in this pipe. Also determine the velocity in 20 cm pipe if the average velocity in 30 cm diameter pipe is $ 2 \, m/s $.

Derive Bernoulli's equation for the flow of an incompressible frictionless fluid from consideration of momentum.

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

Derive an expression for loss of head due to friction in pipes.

A pipe, 100 mm in diameter, has a nozzle attached to it at the discharge end, the diameter of the nozzle is 50 mm. The rate of discharge of water through the nozzle is $ 20 \, litres/s $ and the pressure at the base of the nozzle of $ 5.886 \, N/cm^2 $. Calculate the co-efficient of discharge. Assume that the base of the nozzle and outlet of the nozzle are at the same elevation.

A smooth pipe of diameter 400 mm and length 800 m carries water at the rate of $ 0.04 \, m^3/s $. Determine the head lost due to friction, wall shear stress, centre-line velocity and thickness of laminar sub-layer. Take the kinematic viscosity of water as 0.018 stokes.

Distinguish between: (i) Steady flow and un-steady flow (ii) Uniform and non-uniform flow (iii) Compressible and incompressible flow (iv) Rotational and irrotational flow.

Explain the significance of non-dimensional number: (i) Reynolds number (ii) Froude number (iii) Mach number (iv) Weber number.

A wooden block (of specific gravity 0.70) of size $ 150 \times 15 \times 30 $ cm floats horizontally on the surface of sea water (specific weight $ 1025 \, kg/m^3 $). Calculate the volume of water displaced, depth of immersion and the position of centre of buoyancy. Also find the metacentric height of the block.

Two fluids 1 and 2 have mass densities of $ \rho_1 $ and $ \rho_2 $ respectively. If $ \rho_1 > \rho_2 $, which one of the following expressions will represent the relation between their specific volumes $ v_1 $ and $ v_2 $?

Which one of the following is the dimension of mass density?

Specific gravity is what kind of property?

Which of the following is the dimension of kinematic viscosity?

The rise in the level of a liquid in a tube is h. What will be the rise in the level if the same amount of liquid is poured into a tube of half the diameter?

A hydraulic press has a ram of 30 cm diameter and a plunger of 2 cm diameter. It is used for lifting a weight of 35 kN. Find the force required at the plunger.

Can the flow inside a nozzle be steady and uniform?

What is the maximum number of times the pathlines of two particles can intersect in a one-dimensional flow?

Darcy-Weisbach equation gives relation between

The main property that affects a boundary layer is

State the difference between solid and fluid under the action of various forces.

What is kinematic viscosity? What are its units?

A U-tube is made up of two capillaries of bores 1.2 mm and 2.4 mm respectively. The tube is held vertical and partially filled with liquid of surface tension $ 0.06 \, N/m $ and zero contact angle. If the estimated difference in the level of two menisci is 15 mm, determine the mass density of the liquid.

The velocity distribution in a viscous flow over a flat plate is given by $ u = 4y - y^2 $ where u is the velocity in $ m/s $ at a distance of y metre normal to the plate. If the dynamic viscosity of fluid is $ 1.6 \, Ns/m^2 $, determine the shear stress at $ y = 0 $ m and $ y = 0.1 $ m.

Determine the gauge pressure at point a shown in Fig. 1, if liquid A has $ SG=0.75 $ and liquid B has $ SG=1.20 $. The liquid surrounding point a is water, and the tank on the left is open to the atmosphere.

The tank shown in Fig. 2 is 3 m wide into the paper. Neglecting atmospheric pressure, compute the hydrostatic (i) horizontal force, (ii) vertical force and (iii) resultant force on quarter-circle panel BC.

Derive the expressions for total pressure and centre of pressure for a vertically immersed surface.

The stream function in a two-dimensional, incompressible flow field is given as $ \Psi = A(x^2 - y^2) $.
(i) Determine the velocity components.
(ii) Determine whether the above flow field represents a possible case of an incompressible flow or not.
(iii) Obtain an expression for the velocity potential.

Distinguish among pathlines, streamlines and streaklines.

Petroleum oil (specific gravity = 0.9 and viscosity = $ 0.013 \, Ns/m^2 $) flows isothermally through a horizontal 5 cm pipe. A Pitot tube is inserted at the centre of a pipe and its leads are filled with the same oil and attached to a U-tube containing water. The reading on the manometer is 10 cm. Calculate the volumetric flow of oil in $ m^3/s $. The coefficient of Pitot tube is 0.98.

Describe an orifice meter and find an expression for measuring discharge of fluid through a pipe with this device. List all the assumptions made.

The load carrying capacity W, of a journal bearing is known to depend on its diameter D, length l and clearance c, in addition to its angular speed $ \omega $, and lubricant viscosity $ \mu $. Establish a dimensionless relationship of these parameters with the help of Buckingham's $ \pi $ theorem.

What are meant by geometric, kinematic and dynamic similarities?

What do you understand by total energy line and hydraulic gradient line?

Oil, with $ \rho = 900 \, kg/m^3 $ and $ \nu = 0.00001 \, m^2/s $, flows at $ 0.2 \, m^3/s $ through 500 m of 200 mm diameter cast-iron pipe. Determine (i) the head loss and (ii) the pressure drop if the pipe slopes down at $ 10^{\circ} $ in the flow direction.

Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a diameter of 400 mm. The rate of flow of water through the pipe is $ 250 \, litres/s $.

What is a siphon? On what principle it works?

How would you distinguish between hydrodynamically smooth and rough pipe?

What are meant by scale and intensity of turbulence in turbulent flow?

Two fluids 1 and 2 have mass densities of $ \rho_1 $ and $ \rho_2 $ respectively. If $ \rho_1 > \rho_2 $, which one of the following expressions will represent the relation between their specific volumes $ v_1 $ and $ v_2 $?

Which one of the following is the dimension of mass density?

Specific gravity is what kind of property?

Which of the following is the dimension of kinematic viscosity?

The rise in the level of a liquid in a tube is h. What will be the rise in the level if the same amount of liquid is poured into a tube of half the diameter?

A hydraulic press has a ram of 30 cm diameter and a plunger of 2 cm diameter. It is used for lifting a weight of 35 kN. Find the force required at the plunger.

Can the flow inside a nozzle be steady and uniform?

What is the maximum number of times the pathlines of two particles can intersect in a one-dimensional flow?

Darcy-Weisbach equation gives relation between

The main property that affects a boundary layer is

State the difference between solid and fluid under the action of various forces.

What is kinematic viscosity? What are its units?

A U-tube is made up of two capillaries of bores 1.2 mm and 2.4 mm respectively. The tube is held vertical and partially filled with liquid of surface tension $ 0.06 \, N/m $ and zero contact angle. If the estimated difference in the level of two menisci is 15 mm, determine the mass density of the liquid.

The velocity distribution in a viscous flow over a flat plate is given by $ u = 4y - y^2 $ where u is the velocity in $ m/s $ at a distance of y metre normal to the plate. If the dynamic viscosity of fluid is $ 1.6 \, Ns/m^2 $, determine the shear stress at $ y = 0 $ m and $ y = 0.1 $ m.

Determine the gauge pressure at point a shown in Fig. 1, if liquid A has $ SG=0.75 $ and liquid B has $ SG=1.20 $. The liquid surrounding point a is water, and the tank on the left is open to the atmosphere.

The tank shown in Fig. 2 is 3 m wide into the paper. Neglecting atmospheric pressure, compute the hydrostatic (i) horizontal force, (ii) vertical force and (iii) resultant force on quarter-circle panel BC.

Derive the expressions for total pressure and centre of pressure for a vertically immersed surface.

The stream function in a two-dimensional, incompressible flow field is given as $ \Psi = A(x^2 - y^2) $.
(i) Determine the velocity components.
(ii) Determine whether the above flow field represents a possible case of an incompressible flow or not.
(iii) Obtain an expression for the velocity potential.

Distinguish among pathlines, streamlines and streaklines.

Petroleum oil (specific gravity = 0.9 and viscosity = $ 0.013 \, Ns/m^2 $) flows isothermally through a horizontal 5 cm pipe. A Pitot tube is inserted at the centre of a pipe and its leads are filled with the same oil and attached to a U-tube containing water. The reading on the manometer is 10 cm. Calculate the volumetric flow of oil in $ m^3/s $. The coefficient of Pitot tube is 0.98.

Describe an orifice meter and find an expression for measuring discharge of fluid through a pipe with this device. List all the assumptions made.

The load carrying capacity W, of a journal bearing is known to depend on its diameter D, length l and clearance c, in addition to its angular speed $ \omega $, and lubricant viscosity $ \mu $. Establish a dimensionless relationship of these parameters with the help of Buckingham's $ \pi $ theorem.

What are meant by geometric, kinematic and dynamic similarities?

What do you understand by total energy line and hydraulic gradient line?

Oil, with $ \rho = 900 \, kg/m^3 $ and $ \nu = 0.00001 \, m^2/s $, flows at $ 0.2 \, m^3/s $ through 500 m of 200 mm diameter cast-iron pipe. Determine (i) the head loss and (ii) the pressure drop if the pipe slopes down at $ 10^{\circ} $ in the flow direction.

Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a diameter of 400 mm. The rate of flow of water through the pipe is $ 250 \, litres/s $.

What is a siphon? On what principle it works?

How would you distinguish between hydrodynamically smooth and rough pipe?

What are meant by scale and intensity of turbulence in turbulent flow?