### Few Questions of Fluid Mechanics

1. What are the SI & CGS units of viscosity & kinematic viscosity? What is the relation between the SI & CGS
unit of viscosity? What is the value of viscosity of air & water at 288 K temperature?

2. (a)    Define bulk modulus of elasticity without using any formula?
(b) Bulk modulus of elasticity of water is 2000000 kN/m2.  A pressure of 10 bar is applied on water having
volume of 2m3. Find the  change in volume of water in m3.

3. Find the flux of velocity having the components as 9x, -3y and 0 along the x, y and z axes respectively over
the closed surface of the sphere given by x2 + y2 + z2 = 9.

4.  A flow field is given by u = ay, v = bz & w =cx. Determine whether the flow is rotational or irrorational.

5. The clearance space between a shaft and a concentric sleeve has been filled with a Newtonian fluid. The
sleeve attains a speed of 600 mm/s when a force of 600N is applied to it parallel to the shaft. What force is
needed if it is desired to move the sleeve with a speed of 3m/s?

6. A single column U-tube manometer, made of glass tubing having a nominal inside diameter of 2.5mm, has
been used to measure pressure in a pipe or vessel containing air. If the limb opened to atmosphere is 11%
oversize, find the error in mm of mercury in the measurement of air pressure due to surface tension
effects. It is stated that mercury is the manometric fluid for which surface tension is 0.514 N/m and angle of
contact is 140°.

7. The sea level conditions of the atmosphere are 101.325 KN/m2, 15°C and 1.225 Kg/m3.  Find the pressure
of air 7200 m above the seal level assuming (a) air as incompressible (b) air as compressible that follows the
isothermal law.

8. A piece of 2.5 m long wood of specific gravity of 0.6 having 10 cm2 cross-section is floating in water. How
much lead (specific gravity 12) needs to be fastened at the lower end of the wood so that it floats upright
with 0.5 m length out of water?

9. Velocity of air is 10 m/s. A circular ring of area of 2 sq. m is placed in the flow. Find the volume flow rate of air passing through the ring if the ring is oriented
(a)    Parallel to the flow
(b)   Perpendicular to the flow
(c)    45° to the flow
(d) 30° to the flow

10. (a)     Is the flow field u = t, v = 0 & w = 0 steady or unsteady, uniform or non-uniform? Prove your
(b)   Is the flow field u = 0, v = x & w = 0 steady or unsteady, uniform or non-uniform? Prove your answer.

11.   In a 3-D incompressible flow field,  u = x2 + z2 + 5 and v = y2 + z2 - 3. Derive the expression for the third             component of velocity w.

12.   (a) The velocity field in cm/s   is given by u = y/(x2 + y2) and v = −x/(x2 + y2).  Calculate the
circulation around a circular path of radius 5 m.
(b) The velocity field in cm/s   is given by u = y/(x2 + y2) and v = −x/(x2 + y2).  Calculate the
circulation around a circular path of radius 5 m.

13. A velocity potential for a two dimensional flow is given by the expression φ = x2 – y2.
Find the velocity components u & v, resultant velocity and determine its value at a point (1, 2)
when t =1 & when t = 3.

14. What is a fluid?
15. What is Archimede’s principle?
17. What do you understand by Quasi-1D flow?
18. What is the difference between isothermal & isentropic flow?
19. Explain Newton’s law of viscosity without using any formula.
20. Why does the viscosity of air increase while that of water reduces with increase of temperature?
21. Explain the law of motion on which the Euler’s equation is based.
22.  Explain any two forms of energy stored in a fluid.
23. Can hydrostatic equation be derived from Euler’s equation? If so, how?
24. What do you understand by ‘dimensional homogeneity’?
25. Explain what do you understand by Froude number without using any formula? What is its significance?
25A. Explain what do you understand by Mach number without using any formula? What is its significance?

26.   Use Buckingham’s Pi-theorem to derive a functional relationship between resistance R of a partially submerged body and the other independent variables i.e. reference length of body l, velocity V, fluid viscosity μ, fluid density ρ & acceleration due to gravity g.

27. A horizontal water pipe of diameter 150mm converges to 75 mm diameter. The pressures at the two sections are 400 kPa & 150 kPa respectively. Calculate the water flow rate.

28. A pipe connects a reservoir to a turbine which discharges water to a tail race through another pipe. The head loss between the reservoir and the turbine is 10 times the kinetic head in the pipe and that from the turbine to the tail race is 0.5 times the kinetic head in the pipe. The rate of flow is 1 m3/s. The pipe diameter in both the cases is 1000mm. Energy level EL of turbine, reservoir & tail water are 105 m, 150 m & 100 m respectively.
(a)    Find the pressure at turbine inlet & exit.
(b) Calculate the power generated by the turbine.

29. A pipe of 250 mm diameter, 250 m long carries water from station A to station B located 10 m higher. Shear stress between the liquid and the pipe wall is 25 N/m2.  Calculate the pressure change in the pipe & the head lost.

30. A fireman holds a water hose ending into a nozzle that issues a 2 cm diameter jet of water. If the pressure of water in the 6 cm diameter hose is 700 kPa, what is the force acting felt by the fireman?

31. A closed tank 1 m × 1.25 m in plan × 4.5 m high & weighing 1175 N is filled with water to a depth of 3 m. A hole in one of the side walls has an effective area of 7.5 cm2 and is located 200 mm above the tank bottom. The coefficient of friction between the ground and the wheels is 0.012. Calculate the air pressure needed in the tank to set it into motion.

32. 0.25 m3 water at pressure of 400 kPa flows into a pipe of 300 mm diameter. The pipe has a bend at angle of 135°. Find the magnitude & direction of the resultant force on the bend.

33. An aeroplane with two 215 cm diameter propellers travels through still air (density = 1.22 Kg/m3) at 100 m/s. Discharge through each propeller is 425 m3/s. Find the thrust, power input, theoretical efficiency of propulsion system & the pressure difference across the propeller.

34. A lawn sprinkler with two nozzles of diameter 3.5 mm each is connected across water tap capable of 0.1 litres/s discharge. Both the nozzles discharge water in downward direction & are located at radial distance of 25 cm & 15 cm from the centre of the tap.
(a)    How much torque needs to be applied to hold the rotor stationary?
(b)   What constant speed will the sprinkler reach?
Neglect the bearing friction and assume equal discharge rate of the nozzles.

35. A water jet issues out from a nozzle which is inclined at 45° to the horizontal & is held at level 3 m above the ground. Observations indicate that the jet strikes the ground at a horizontal distance of 15 m from the nozzle. Calculate
(a)    Velocity of jet
(b)   Maximum height reached by the fluid particles
(c)    Location of topmost point.
Neglect air resistance.

36. A cylinder containing oil of sp. gr. 0.85 is rotated about its vertical axis with constant angular velocity. Pressure measurements indicate equal pressures at two points 1 & 2 which are respectively at 500 mm & 750 mm radial distance from the axis of rotation. If point 2 lies 1 m above the point 1, calculate the rotational speed in RPM.

37. Water flows radially outwards between two horizontal circular flat plates of 25 cm diameter, placed 0.8 cm apart. The plates are submerged in water at a depth of 2.5 m measured from the free water surface to the centre of parallel plates. Water enters the system through a 120 mm diameter pipe at the centre of lower plate at a pressure of 60 kPa. Make calculations for the peripheral discharge and thrust on the upper & bottom plates. Ignore the dynamic force of the entering water and take atmospheric pressure as 100 kPa and the specific weight of water as 10 kN/m3.

38. Use Buckingham’s Pi-theorem to derive a functional relationship between drag F of a supersonic plane and the other independent variables i.e. reference length of aeroplane l, velocity V, air viscosity μ, air density ρ & bulk modulus of air K.

39. A 2.5 m ship model was tested in fresh water and measurements indicated that there was resistance of 45 N when the model moved at 2 m/s.  For dynamic similarity, what should be the velocity of the prototype? How much force would be needed to drive the prototype at this speed through sea water (density = 1025 Kg/m3).

40. A model of a torpedo is tested in a towing tank at a velocity of 26 m/s whilst the prototype is to run at 6.5 m/s.
(a)    What model scale has been used? For water, kinematic viscosity is 1.13 × 10-4 m2/s.
(b) What would be the model speed if tested in wind tunnel under a pressure of 2000 kPa and a constant temperature of 300 K. Viscosity of air is 1.85 × 10-4 poise. R = 287 J/Kg K.

41. What happens when the  critical Reynolds number is reached in a flow?
42. What do you understand by plane Couette low?
43.  On which equation/principle does the manometer work?
44. What do you understand by a ‘streamlined body’ and a ‘bluff body’?
45. How does circulation create lift on a moving body?
46. Explain ‘Magnus effect’?

47. (a)  Draw the flow streamlines around
(i)      Circular disc
(ii)    Sphere
(iii)   Streamlined body
placed in a real flow.
(b)  Which of the above-mentioned body will have maximum pressure drag as its percentage of total drag? Why?
(c)  Which of the above-mentioned body will have maximum skin friction drag as its percentage of total drag? Why?

48. (a)    Draw the flow streamlines around an aerofoil section placed in the real flow.
(b)   Draw the pressure distribution around this aerofoil section.
(c)    Draw the graph of pressure coefficient versus chord percent for both the upper and the lower surfaces of the aerofoil.

49. Draw the diagrams of the following and label the various parts:-
(i)                  Piezometer
(ii)                U-tube double column manometer
(iii) Vane anemometer

50. Draw the diagrams of the following and label the various parts:-
(i)                  Current meter
(ii)                Straight single column manometer
(iii) Cup  anemometer

51. Draw the diagrams of the following and label the various parts:-
(i)                  Piezometer
(ii)                Inclined single column manometer
(iii) Turbine meter

52. Experiments were conducted in a wind tunnel at speed of 50 kmph on a flat plate 2 m long and 1 m wide placed at an angle to the incoming air. Density of air is 1.15 Kg/m3. Coefficients of lift and drag are 0.75 and 0.15 respectively. Determine the lift force, drag force, resultant force (its direction also) and power exerted by the air stream on the plate.

53. A jet plane having a wing area of 20 m2 and weighing 25 kN flies at 950 kmph. The engine develops 8500 kW and has mechanical efficiency of 60%. Determine the lift and drag coefficients. Density of air is 1.225 Kg/m3.

54. A passenger car with frontal projected area of 1.5 m2 travels at 56 kmph. Determine the power required to overcome wind resistance if the drag coefficient of the car is 0.4.
For the same power expended in overcoming resistance, what percentage change in the speed of the car is possible if drag coefficient is reduced to 0.32 by streamlining the car body?

55.  An 8 mm ball made of a material of relative density 1.25 is suspended from a string. Wind flows past the ball at a velocity of 10 m/s. Calculate the angle which the string makes with the vertical. For air, density is 1.225 kg/m3 and viscosity is 1.8×10-5 N-s/m2.

56. (a)    Determine the velocity of fall of rain drops of 0.3 mm diameter in atmosphere air having density of 1.2 Kg/m3 and kinematic viscosity of 0.15 cm2/s.
(b)   Which has a higher terminal velocity: 1mm air bubble rising in fresh water or a 1 mm water droplet falling in air? Estimate the ratio of their terminal velocities from the data given below:
Viscosity: air 1.86×10-5 N-s/m2, water 1.01×10-3 N-s/m2
Density: air 1.2 Kg/m3, water 1000 Kg/m3.

57. A container full of oil has a horizontal parallel crack in its end wall which is 500 mm wide and 50 mm thick in the direction of the flow. The pressure difference between two faces of the crack is 10 kPa and the crack forms a gap of 0.4 mm between the parallel surfaces. Calculate
(i)                  Volume of oil leakage per hour through the  crack
(ii)                Maximum leakage velocity
(iii)               Shear stress and velocity gradient at the boundary
Take sp. gr. And viscosity of the oil as 0.85 and 1.8 poise respectively.

58. At what distance r from the centre of a pipe of radius R does the average velocity occur in laminar flow?
Water is flowing through a 20 cm diameter pipe with friction factor f = 0.04. The shear stress at a point 4 cm from the pipe axis is 100 Pa. Calculate the shear stress at the pipe wall.

59. A turbulent flow of water occurs in a pipe of 0.6 m diameter. The velocity profile is measured experimentally and found to be  u = 3 + (logey)/3 m/s. y is the distance from the wall in m. The shear stress at a point 0.1 m from the wall is 10 N/m2. Find the turbulent viscosity , the mixing length and the turbulence constant k.

60. The right limb of the U-tube manometer containing Mercury is open to the atmosphere while the left limb is connected to a pipe through which flows a fluid of sp. gr. 0.85. The centre of the pipe lies 15 cm below the level of mercury in the right limb. If the difference of mercury level in the two limbs is 25 cm, determine the pressure of fluid of pipe.

61. Water discharges at the rate of 98.2 litres per second through a 12 cm diameter vertical sharp edged orifice placed under a constant head of 10 m. A point, on the jet measured from vena-contracta has co-ordinates 4.5 m horizontal and 0.54 m vertical. Find the hydraulic coefficients Cv, Cc & Cd.

62. Draw the diagrams of the following and label the various parts:-
(i)                  Piezometer
(ii)                U-tube double column manometer
(iii) Vane anemometer
(iv) Current meter
(v) Straight single column manometer
(vi) Cup anemometer
(vii) Inclined single column manometer
(viii) Turbine meter

1. I ve used gauss divergence in 3rd problem and answer is 27 is it correct?

1. 2. Rate of change of temperature(Temperature Lapse rate) in troposphere is
A) 2 degree celcius/ km
B) 3.5 degree celcius/km
C) -2.2 degree celcius/ km
D) -6.5 degree celcius/km

The correct answer is -2 degrees C per 1000 ft or -6.5 degrees C per km.

3. Doubt:-Is it possible to have concavity and a point of infection at any point, in case of a stream line and equipotential line?

1. Let us say the stream function or potential function is cube of x. Then at x =o, we have the inflexion point (second derivative is zero and it changes its sign while passing through this point). The curve changes from convex to concave.

Thus theoretically, it is possible according to me.
But it may be more complicated. Do let me know, if you find something more.

2. 4. This comment has been removed by the author.

5. Q. 39:) I think data insufficient.

1. Length of the prototype may be assumed as L

6. Can i get the solution of question no.31