1. A tank of water with uniform area of cross section A has a hole at its bottom with an area of a.There was a water column of 4 m height in the tank initially.It took 5 second for the water level in the tank to reduce to 1 m.How long did it take totally to empty the whole tank?

2. What are the dimensions of surface tension?

3. The specific gravity of oil is 0. Calculate the pressure represented by a 5 cm column of oil.

4. Which of the following statements about viscosity is true?

5. Which of the following is NOT a dimensionless number?

6. Which of the following is the definition of Froude number?

7. Calculate the speed of sound in an ideal gas (γ = 1.4) at temperature 273°K.

8. What does the Reynolds number measure?

9. Consider a steady incompressible flow with velocity field: u(x, y, z) = 3x + y + z, v(x, y, z) = -y + 5x + 3z, w(x, y, z) = Cz + x + y, where C is a constant.Calculate the value of C so the given flow is physically possible.

10. Consider water flowing through a 10 m section of 4 inch ID smooth pipe followed by an abrupt contraction to a 1 m section of 0.25 inch IDsmooth pipe. If the water is flowing at 2 gal/min, calculate the total pressure drop over the two sections (remember to include the effect of the contraction).

11. Air flows over a sharp flat plate with a velocity of 2.5 m/s. Calculate the thickness of the boundary layer about 50 cm away from the edge. Density and kinematic viscosity of air are 1.2 kg/m³ and 1.5 10^-5 m²/s, respectively.

12. Which of the following is a streamline?

13. Consider a steady, incompressible flow with a velocity distribution given as V = axi + byj + 0k, where a and b are constants.What is the relationship between a and b required to satisfy the principle of mass conservation?

14. What does the Froude number measure?

15. Fully developed, laminar flow of a Newtonian fluid in a round pipe is well—described by

Use this expression to calculate the product τ_rz 2 π R (where τ_rz = μ dv/dr) for a Newtonian fluid evaluated at the pipe wall. Which of the following expressions matches your result?

16. For laminar flow of a Newtonian fluid in a circular pipe, calculate the ratio of the maximum or peak fluid velocity to the cross-sectional average velocity. Which of the following numbers best represents that ratio?

17. For fully turbulent flow of a Newtonian fluid in a circular pipe and moderate Re, the velocity profile can well—approximated by v/v_max = (1-r/R)^(1/n) , with n=7. Calculate the ratio of the largest or peak fluid velocity to the cross-sectional average velocity. Which of the following numbers best represents that ratio?

18. What does a barometer measure?

19. What is the pressure on a given object?

20. Capillary viscometer.
You have already measured the density of an unknown fluid and found it to be 1.35 g/ml. You wish to determine the fluid viscosity from measurement of the pressure drop through a 1 mm ID by 1 m long capillary as a function of the flow rate. For a flow rate of 45 ml/min, you find the pressure drop to be.
Which of the following is the best estimate of the fluid viscosity?

21. A water jet strikes normal to a fixed vertical plate.The diameter of the jet is 2 cm.The velocity is 1 m/s.What is the force of the jet acting on the plate?(Hint: Neglect friction and gravitation forces.)

22. Water flows in a pipe with a roughness ε of 8 10^-4 ft. The diameter D of the pipe is 1 inch. The flow velocity is 30 ft/s. The kinematic viscosity of water is 4.38 x 10^-6 ft²/s. Determine the friction factor.

23. For a laminar pipe flow, how does the friction factor change when the Reynolds number increases?

24. What is the shear stress τ_xy at point (x, y, z) of an incompressible fluid flow with the following velocity distribution V = 5xi + 6yj + 0k? The viscosity of the fluid is µ.

25. Terminal velocities of spheres.
Calculate the approximate terminal velocities of a bowling (US) ball and a table-tennis (ping-pong) ball falling through air under the acceleration of gravity. The properties of the balls and air are summarized below. You may assume that gravity has an acceleration of 9.8 m/s², that the air is stagnant, and that the drag over a sphere is well represented by the curves in this link from NASA.
Properties of air at 20 C: ρ=1.2 kg/m³; k=0.026 W/m K; υ=15 x 10^-6 m²/s.
Bowling Ball: d=8.5 inches; m= 14 lb. The ball is smooth.
Table Tennis Ball: m=2.7g; d = 40 mm. The ball is smooth.
Which of the following pairs of numbers best represent the terminal velocities of the bowling ball and the tennis ball, respectively, in miles per hour?