Reynold's Model Law

Q. A 1:30 scale model of a submarine is to be tested in a wind tunnel for its drag when it is operating at 15 km/h in ocean. The kinematic viscosity of air is 1.51$\times {10}^{-5}{m}^2/s$ and for water $1.02\times {10}^6{m}^2/s.$ What is the velocity of air in wind tunnel that should be maintained for kinematic similarity?

1. 1500 m/s
2. 2000 m/s
3. 1850.5 m/s
4. 2500.5 m/s

Q. The flow of glycerin (kinematic viscosity $v=5\times {10}^{-4}{m}^2/s$) 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?

1. 1
2. 22
3. 63
4. 500

Q. Water having kinematic viscosity of 0.01 stokes flows at a velocity of 2 m/sec in a pipe of 15 cm diameter. For dynamic similarity, the velocity of oil of kinematic viscosity 0.03 stoke in a pipe of same diameter will be

1. 0.33 m/sec
2. 0.66 m/sec
3. 2 m/sec
4. 6 m/sec

Q. The Reynolds number for flow of a certain fluid in circular tube is specified as 2500. What will be the Reynolds number when the pipe diameter is increased by 20% and the fluid velocity is decreased by 40% keeping fluid the same?

1. 200
2. 1200
3. 1800
4. 3600

Q. A sphere is moving in water with a velocity of 1.6 m/s. Another sphere of twice the diameter is placed in a wind tunnel and tested with air which is 750 time less dense and 60 times less viscous (dynamically) than water. The velocity of air that will model dynamically similar conditions is

1. 5 m/s
2. 20 m/s
3. 10 m/s
4. 40 m/s

Q. Which of the following is a dimensionless parameter?

1. Linear velocity
2. Gravity force
3. Reynold's number
4. Viscosity

Q. Which of the following statements are correct ?
1. Depression of mercury in a capillary tube is dependent on density and surface tension.
2. Modelling of flow-induced drag on a ship is done invoking both of Froude number and Reynolds number.
3. Flow of a fluid in a narrow pipe is relatable to both Reynolds number and Cauchy number.
4. Formation and collapse of a bubble is analyzed through employing surface tension and external pressure.
5. Flow over the downstream slope of an ogee spillway can be affected can be affected by surface tension.
Select the correct answer using the codes given below:

1. 1, 2 and 4
2. 1, 3 and 5
3. 2, 3 and 4
4. 3, 4 and 5

Q.

Air is escaping from a balloon at the rate of $\mathrm{R}\left(\mathrm{t}\right)=\frac{60}{1+{\mathrm{t}}^2}{\mathrm{ft}}^3/\min$ , where $t$ is measured in minutes. How much air, in cubic feet, escapes during the first minute​?