MODULE- 64C. Dimensional analysis and hydraulic modeling. As gravitational force is predominant, Froude model law has to be applied.

Transcription

1 MODULE- 64C Dimensional analysis and hydraulic modeling. 1. In a 1/50 model of a spillway, the discharge was measured to be 0.3. The corresponding prototype discharge in is (A) 2.0 (B) 15.0 (C) (D) As gravitational force is predominant, Froude model law has to be applied. 2. A laboratory model of a river is built to a geometric scale of 1:100. The fluid used in the model is oil of mass density 900 kg/m 3. The highest flood in the river is 10,000 m 3 /s. The corresponding discharge in the model shall be (a) 0.95 m 3 /s. (b) m 3 /s. (c) m 3 /s.(d) 10.5 m 3 /s. As gravitational force is predominant, Froude model law has to be applied. JH ACADEMY Page 1

2 = 3. The height of a hydraulic jump in the stilling pool of 1.25 scale model was observed to be 10 cm. The corresponding prototype height of the jump is (a) not determinable from the data given (b) 2.5 m c) 0.5 m (d) 0.1 m =250 cm =2.5 m 4. The flow of glycerin (kinematic viscosity v = m 2 /s) in an open channel is to be modeled in a laboratory flume using water (v=10-6 m 2 /s) as the flowing fluid. If both gravity and viscosity are important, what should be the length scale (i.e. ratio of prototype to model dimensions) for maintaining dynamic similarity? (a) 1 (b) 22 (c) 63 (d) 500 From Froude model law From Reynolds model law =1 Substituting for =1 = JH ACADEMY Page 2

3 5. A 1: 50scale model of a spillway is to be tested in the laboratory. The discharge in the prototype is The discharge to be maintained in the model test is (a) (b) (c) (d) 5.7. As gravitational force is predominant, Froude model law has to be applied. = 6. A river reach of 2.0km long with maximum flood discharge of 10000m 3 /s is to be physically modeled in the laboratory where maximum available discharge is For a geometrically similar model based on equality of Froude number, the length of the river reach (m) in the model is (A) 26.4 (B) 25.0 (C) 20.5 (D) Group-I contains dimensionless parameters and Group- II contains the ratios. Group-I Group II P. Mach Number 1. Ratio of inertial force and gravitational force Q. Reynolds Number 2. Ratio of fluid velocity and velocity of sound R. Weber Number 3. Ratio of inertial force and viscous force S. Froude Number 4. Ratio of inertial force and surface tension force The correct match of dimensionless parameters in Group- I with ratios in Group-II is: JH ACADEMY Page 3

4 (A) P-3, Q-2, R-4, S-1 (B) P-3, Q-4, R-2, S-1 (C) P-2, Q-3, R-4, S-1 (D) P-1, Q-3, R-2, S-4 Ans (C) 8. A 1:10 scale model of sub marine moving for below the surface of water is tested in a water tunnel. If the speed of prototype is 8m/sec. determine the corresponding velocity of water in tunnel. Also determine the ratio of drag for the model and prototype. Kinematic viscosity of sea water is, and that of water is. = 1027kg/, =1000kg/ (A) (B) 77.4 (C) 7.74 (D) 18.0 As viscosity is predominant force Reynolds model law is applicable. Drag force F= = A single pipe of length =1500m and diameter 60cm connects two reservoirs having difference of 20m in water level. The pipe is to be replaced by two pipes of same length and equal diameter d to convey 25% more discharge under same head loss. So the dia is? (A) 1.0 (B) 0.5 (C) 1.5 (D) 2.0 JH ACADEMY Page 4

5 Discharge per pipe = 10. A 1:50 scale model of spillway is to be tested in laboratory. The discharge in prototype is What is the discharge in model? (A) 5.64 (B) 5.64 (C) 5.64 (D) 5.64 As gravitational force is predominant, Froude model law has to be applied. Froud number = = 11. The height of hydraulic jump in a stilling pool of 1:25 scale model was observed to be 10cm. the corresponding prototype height of jump is (A) 1.0 (B) 0.5 (C) 1.5 (D) Water at flows at 4m/s in a 150mm pipe. At what velocity must oil at C flow in a 75mm pipe for the two flows to be dynamically similar? Take for water at as and that for oil at C as (A) (B) (C) 1.5 (D) 30.2 JH ACADEMY Page 5

6 As viscosity is predominant force Reynolds model law is applicable. 13. A 1/6 model automobile is tested in a wind tunnel with same air properties as the prototype. The prototype automobile runs on the roads of velocity of 60 km/hr. for dynamically similar conditions, the drag measured on the model are 500N. determine the drag of the prototype and the power required to overcome the drag (A) 500N, 8.33KN (B) 400N, 8.33KN (B) 500N, 9.33KN (D) 600N, 8.33KN As viscosity is predominant force Reynolds model law is applicable. Drag on prototype =500N 14. A hydraulic jump occurring in a stilling basin is to be studied in a 1:36 scale model. The prototype jump has an intial velocity of 10m/s, an entrance Froude number of 6.0 and power loss of 2kw per meter width of basin. Determine the corresponding model velocity, model Froude number and power loss per meter width of the model (A) 1.67m/s, 6.0, 0.26w (B) 1.67m/s, 4.0, 0.26w (C) 2.67m/s, 6.0, 0.26w (D) 1.67m/s, 6.0, 2.6w JH ACADEMY Page 6

7 As gravitational force is predominant, Froude model law has to be applied. Froud number = Froude number is same in model and prototype. Power = 15. A model of a reservoir having a free water surface within it is drained in 3 minutes by opening a sluice gate. The geometrical scale of the model is. How long would it take to empty the prototype (minutes) (A) 120 (B) 20 (C) 30 (D) 10 As gravitational force is predominant, Froude model law has to be applied. JH ACADEMY Page 7

8 16. Water flows through valve having 0.8m diameter at a rate 85. It is to be tested in a geometrically similar model of 10cm diameter with water as working fluid. Determine the required flow rate in the model in (A) 12.7 (B) 10.6 (C) 8.4 (D) A spillway model of 1:10 scale is constructed to study the flow characteristics for a prototype dam of width 10m and to carry water at a flow rate of 60. Determine the required model width and flow rate. What operating time for the model corresponds to a 24hr period in prototype? (A) 0.19, 7.6 (B) 1.9, 76 (C) 19, 7.6 (D) 19, 76 As gravitational force is predominant, Froude model law has to be applied. JH ACADEMY Page 8

9 = 0.19 = = =24*0.316 =7.58 h 18. A 1:30 scale model of a submarine is to be tested in a wind tunnel for its drag when it is operating at 15Km/h in ocean. The kinematic viscosity of air is 1.51 and for water What is the velocity of air in wind tunnel that should be maintained for kinematic similarity? a) 1500m/s b) 2000m/s c) m/s d) m/s As viscosity is predominant force Reynolds model law is applicable. 15 kmph=4.1667m/s 19. Which one of the following statements is not correct? a) Models are always smaller than the prototypes b) Dynamic similarity between a model and a prototype can be verified by equating Reynolds number in a viscous flow. c) Mach number achieves significance when the velocity of fluid approaches or exceeds the sonic velocity. d) Distorted models are always exaggerated on a vertical scale. (a) JH ACADEMY Page 9

10 20. A river model is constructed to a horizontal scale of 1:1000 and a vertical scale of 1:100. A model discharge of 0.1 would correspond to a discharge in the prototype, of what magnitude? a) b) c) d) As gravitational force is predominant, Froude model law has to be applied. 21. For a homologous model of a pump built to a scale ratio of 1:2, fluid and speed being the same in model and prototype, the ratio of model power to prototype power is a) b) c) d) P P As speed is same H 22. Distorted models are needed for: 1. Rivers 2. Dams across wide rivers 3. Harbours a) 1 and 2 only b) 2 and 3 only c) 1 and 3 only d) 1, 2 and 3 (d) JH ACADEMY Page 10