Birla Institute of Technology and Science, PilaniFirst Semester, 2015-16

CHE F212, Fluid MechanicsComprehensive Examination 11th December, 2015Max Time: 180 min Total Max Points: 105 This question paper is divided in two parts; A & B. Part A will be answered in question paper itself. Use answer sheets only for part B. Return part A and the answer sheet separately; do not tie them together.

SECTION A (55 Marks)

Q1: Fill in the blanks. Write only the right word(s). Negative marking is applied [0.5 x 20]

1. CD ∞ corresponds to FD ∞ V, and if CD is , then FD ∞ V2

2. boundary-layer flow is desirable on a blunt body because it delays separation and thus -

the pressure drag

3. With velocity of-approach factor mean mass flow rate

4. In case of using a combined Pitot tube for flowing fluid pressure measurement, the static pressure hole

should be situated at to the stagnation pressure hole and the flow .

5. For a radial pump the flow coefficient linearly as the radius of the impeller outlet diameter

.

6. Literally speaking, the relation between and viscosity of a fluid is proportional in

general.

7. Taylor series is an sum giving the value of a function f(z) in the neighborhood of a point 'a' in

terms of the of the function evaluated at 'a'.

8. substantial derivative can be used to express ______ of energy of a particle floating along

with a flow.

9. At very low Reynolds number, , there is flow separation from a sphere;

10. Low specific speeds correspond to efficient operation of machines, whereas, high specific

speeds correspond to efficient operation of machines.

11. Adverse gradient supports the boundary layer .

12. In case of inviscid flow, there will be drag on an object flowing through a fluid, because of the

of boundary layer.

13. For a pump the corresponds to the head developed at flow rate.

1

14. The drag coefficient for all objects with sharp edges is essentially independent of for Re >1000

because the and therefore the size of the wake are fixed by the geometry of the object.

15. for a centrifugal pump results from a between the direction of the relative velocity

and the tangent to the impeller blade at the inlet.

16. can occur in any machine handling liquid whenever the local static pressure falls below the

of the liquid.

17. For a centrifugal pump, specific speed may be consider as the operating speed at which pump produce

unit at unit .

18. Momentum Integral Equation is valid both for and turbulent ______________

19. For outlet vanes the H vs. Q Performance Characteristics curve of a centrifugal pump should be

a straight line to the X-axis.

20. For a centrifugal pump both and leakage loss increase with .

Q2: Multiple choice: Cross the right one only. Multiple cross will reward no marks. [1 X 20]

1. The flowmeters, in terms of the consumption of the fluid energy can be arranged as follows;a. Flow Nozzle= Orifice meter> venturi meterb. Orifice meter> flow Nozzle > venturi meter c. Flow Nozzle> Orifice meter= venturi meterd. Orifice meter< flow Nozzle< venturi metere. There is no particular order.

2. For a centrifugal pump,a. The rate of work done on pump shaft should be greater than zero and the angular momentum of

the fluid may or may not increaseb. The rate of work done on pump shaft should be less than zero and the angular momentum of the

fluid must not increasec. The rate of work done on pump shaft should be greater than zero and the angular momentum of

the fluid must increased. The rate of work done on pump shaft should be greater than zero and the angular momentum of

the fluid must decreasee. The rate of work done on pump shaft should be less than zero and the angular momentum of the

fluid must not decrease

3. Energy Grade Line (EGL) in a flow isa. (pressure energy- kinetic energy + potential energy)/mass of flowb. (pressure energy + kinetic energy + potential energy)*mass of flowc. (pressure energy + kinetic energy - potential energy)/mass of flowd. (pressure energy + kinetic energy + potential energy)/mass of flowe. (pressure energy + kinetic energy - potential energy)*mass of flow

2

4. Theoretically, the fluid mass flow rate along a pipe is measured by the restriction flow meters based on the fact that

a. The fluid mass flow rate is proportional to the pressure drop between pipe and vena contractab. Square of the fluid volumetric flow rate is proportional to the pressure drop between pipe and

meter throatc. Volumetric flow rate of the fluid is proportional to the pressure drop between pipe and meter

throatd. Square of the fluid mass flow rate is proportional to the pressure drop between pipe and meter

throate. Square of the fluid mass flow rate is proportional to the pressure drop between pipe and vena

contracta

5. In case of a centrifugal turbo machine, the flow path is a. Essentially radial, with significant changes in radius from inlet to outletb. Essentially axial, with significant changes in radius from inlet to outletc. Essentially radial, with no changes in radius from inlet to outletd. Essentially axial, with no changes in radius from inlet to outlete. Undefined, with no changes in radius from inlet to outlet

6. For Pumps the steps of fluid energy changes are a. Increase the flow kinetic energy decelerate the flow increase flow pressureb. Decrease the flow kinetic energy decelerate the flow increase flow pressurec. Increase the flow kinetic energy decelerate the flow decrease flow pressured. Decrease the flow kinetic energy decelerate the flow decrease flow pressuree. Increase the flow kinetic energy accelerate the flow increase flow pressure

7. As specific speed of a centrifugal pump increasesa. Both pump capacity & efficiency decreaseb. Pump capacity increases, but efficiency increasec. None of the Pump capacity & efficiency changed. Both pump capacity & efficiency may increasee. Pump capacity decreases, but efficiency increase

8. NPSH Available from the system can be increased by a. using a tortuous pump suction pipe of large diameter and heating fluid b. using a tortuous pump suction pipe of small diameter and heating fluidc. using a short & straight pump discharge pipe of large diameter and cooling fluidd. using a straight pump suction pipe of large diameter and heating fluide. using a short & straight pump suction pipe of large diameter and cooling fluid

9. For a centrifugal pump, the best efficiency point corresponds toa. Shock and recirculation loss at the Lowest, but not the Shock lossb. Highest Shock loss and Friction loss, but lowest recirculation lossc. Lowest Shock loss and Friction loss, but highest recirculation lossd. Lowest Shock, Friction, and recirculation losse. Lowest recirculation loss zero.

10. Stress vs. strain rate of the pseudo plastic and dilatants fluids can be expressed by the same power law. Only difference is that the power term is

a. > 1 for pseudo plastics and <1 for dilatantsb. ≥ 1 for pseudoplastic and < 1 for dilatantsc. >1 for dilatants and < 1 for pseudoplastic d. ≥ 1 for dilatants and > 1 for pseudoplastic

3

e. ≥ 1 for dilatants and ≤ 1 for pseudoplastic

11. If we take two geometrically exact same centrifugal pump of diameters D1= 5m and D2= 15 m thena. Q1/Q2 = 0.04; H1/H2= 0.11; P1/P2=0.004b. Q1/Q2 = 0.4; H1/H2= 11; P1/P2=0.04c. Q1/Q2 = 0.04; H1/H2= 1.1; P1/P2=0.004d. Q1/Q2 = 0.04; H1/H2= 0.11; P1/P2=0.04e. Q1/Q2 = 0.004; H1/H2= 0.11; P1/P2=0.004f. Q= Inviscid flow rate, H= Pump head, P= power

12. The power-law profile of turbulent flow along a pipe cannot be used in calculations of wall shear stress, because

a. It gives an negative velocity gradient at the wallb. It gives an zero velocity gradient at the wallc. It gives an unstable velocity gradient at the walld. It gives an infinite velocity gradient at the center of the flow.e. It gives an infinite velocity gradient at the wall

13. For flowing fluid in a pipea. (kinetic energy coefficient)laminar = (kinetic energy coefficient)turbulent = 1b. (kinetic energy coefficient)laminar = (kinetic energy coefficient)turbulent = 0.2c. (kinetic energy coefficient)laminar > (kinetic energy coefficient)turbulent.d. (kinetic energy coefficient)laminar < (kinetic energy coefficient)turbulente. (kinetic energy coefficient)laminar ≤ (kinetic energy coefficient)turbulent

14. If we consider flow of a spherical object through a fluid, then the point of maximum velocity on the sphere will be at

a. 120º position of the flow directionb. 90º position of the flow direction c. 80º position of the flow direction d. 145º position of the flow direction e. 160º position of the flow direction

15. Example of the turbo-machine for which W and T both are negative a. fansb. compressors c. pumps d. Hydraulic Turbinese. All of the above

16. Small raindrops (radius < 1 mm) falling through atmosphere are spherical; larger ones assume a shape more like that of a hamburger bun. This is the combined effect of

a. drop surface tension and air dragb. drop surface tension, drop weight, and air dragc. drop surface tension and weightd. drop weight and air drage. None of the above

17. Generally, which one of the following is true?a. (displacement thickness/ momentum thickness) for laminar boundary layer >  (displacement

thickness/ momentum thickness) for turbulent boundary layerb. (displacement thickness/ momentum thickness) for laminar boundary layer =  (displacement

thickness/ momentum thickness) for turbulent boundary layer

4

c. (displacement thickness/ momentum thickness) for laminar boundary layer <  (displacement thickness/ momentum thickness) for turbulent boundary layer

d. (displacement thickness/ momentum thickness) for laminar boundary layer >  (displacement thickness/ momentum thickness) for turbulent boundary layer>1

e. displacement thickness/ momentum thickness) for laminar boundary layer =  (displacement thickness/ momentum thickness) for turbulent boundary layer =1

18. After crossing the minimum fluidization velocity, as V 0 increases,a. ∆P across the bed remain constant, but the bed height may decreaseb. ∆P across the bed decreases, but the bed height may increasec. Both ∆P across the bed and the bed height may increased. ∆P across the bed remain constant, but the bed height may increasee. Both ∆P across the bed and the bed height may remain constant

19. At the point of incipient fluidization which of the following relations is valid?a. Pressure drop across the bed = total drag on the particles = the weight of the bedb. Pressure drop across the bed = total drag on the particles = the weight of the bed - buoyant force

of displaced fluidc. Pressure drop across the bed - total drag on the particles = the weight of the bed - buoyant force

of displaced fluidd. Pressure drop across the bed - buoyant force of displaced fluid = total drag on the particles - the

weight of the bede. Pressure drop across the bed = total drag on the particles - the weight of the bed-buoyant force of

displaced fluid

20. At very low velocity of fluid over a smooth sphere, CD is ∞ 1/Re which could be shown theoretically by using

a. Navier Stokes equationsb. Newton's Lawc. Stokes' Lawd. Ergun Equatione. bernoulli's theorem

5

Q3: Conceptual Questions. Marks will be awarded only based on conceptual clarity. Unnecessary discussion will deduct marks. [4 x 6]

1. Prove mathematically that specifying U(x) is equivalent to specifying the pressure gradient for a inviscid flow outside the boundary layer .

2. Use appendix D in Fox ed 8 and suggest the probable pumps for H=33m and Q= 96m3/h system requirment. Mention P, NPSHA, NPSHR, D, ω etc. Is it possible to use this pump for system head 66m? How?

3. backward curved, forward curved, or radial, which type of impeller blade is preferable for industrial use? why? Answer within 2-3 lines only, with proper equations/graphs

6

4. Prove (only mathematically) that for a uniform flow along an infinite flat plate flow separation in the boundary layer is not possible with Zero Pressure Gradient.

5. Laminar boundary layer or turbulent boundary layer, which one is preferable for which kind geometric shape of the moving body through a fluid? Answer within 2-3 lines only, with proper equations/graphs.

6. In general, for rounded pipe entrances, as r/D value increases minor loss decreases, but that is not true for the pipe bends. Explain with right equations/graphs.

7

Birla Institute of Technology and Science, PilaniFirst Semester, 2015-16

CHE F212, Fluid MechanicsComprehensive Examination 11th December, 2015Max Time: 180 min Total Max Points: 105 This question paper is divided in two parts; A & B. Part A will be answered in question paper itself. Use answer sheets only for part B. Return part A and the answer sheet separately; do not tie them together.

The simplest form of the solution will be credited Follow the notations mentioned in question. Don't change Write the assumptions. Cut the rough & the wrong parts clearly Untidy writing will be less credited Box the final answers

SECTION B (50 marks)

Q1: As shown in figure 1, a centrifugal pump with 11.25" (0.28575 m) impeller diameter, is used to pump water at 25°C from a reservoir whose surface is 4.0' (1.2192 m) above the centerline of the pump inlet. The piping system from the reservoir to the pump consists of 10.5' (3.2004 m) of pipe with an ID of 4.0" (0.1016 m) and an average inner roughness height of 0.02" (0.000508 m). There are several minor losses: a sharp-edged inlet (KL = 0.5), three flanged smooth 90° regular elbows (KL= 0.3 each), and a fully open flanged globe valve (KL= 6.0). a) Calculate the maximum volume flow rate (in units of

m3/hr) that can be pumped without cavitation. [10]b) If the water temperature was 60 C, would this maximum

flow rate increase or decrease? Why? [2] Figure 1c) Discuss specifically how you might increase the maximum

flow rate while still avoiding cavitation. [3]Use Figure 3 for the getting NPSHR

Q2: Standard air (temperature at 15 C) flows over a horizontal smooth flat plate at freestream speed U=40 m/s. The plate length is L = 2.5 m and its width is b = 0.8 m. The pressure gradient is zero. The boundary layer is tripped so that it is turbulent from the leading edge; the velocity profile is well represented by the 1/6-power expression. a) Derive the expression for δ as a function of plate length (x) by using Momentum Integral Equation, and

evaluate the boundary-layer thickness, δ, at the trailing edge of the plate. [10]b) Calculate the wall shear stress at the trailing edge of the plate. [2]c) Estimate the skin friction drag on the portion of the plate between x = 0.5 m and the trailing edge [3]

Q3: Catalog data for a centrifugal water pump at design conditions are Q=57 m3/h and ∆p = 128kPa at 1750 rpm. A laboratory flume requires 45 m3/h at 9.8 m of head. The only motor available develops 2.2 kW at 1750 rpm. a) Is this motor suitable for the laboratory flume? Explain with proper calculation. [4]b) How it is possible to use the same pump/motor match here? [6]Hint: Use Fig. 10.9 of Fox (ed 8)

8

Q4: Water flows from a large tank as shown in Fig. below. Atmospheric pressure is 99973.98 Pa and the vapor pressure is 11031.6 Pa. If viscous effects are neglected, a) At what height, h (in mm), will cavitation begin? [8]b) What should be the relative value of D1 and D2 to avoid cavitation, should the value of be increased or decreased? Explain with proper logic. [2] Figure 2

Figure 3

9