2014 Fluid Mechanics Midterm Exam  
When is the most convenient time for you?
Friday Oct 31st, 4pm  33% of the voters. 13% of the votes.    14
Saturday Nov 1st, 10am  33% of the voters. 13% of the votes.    14
Sunday Nov 2nd, 7pm  42% of the voters. 16% of the votes.    18
Monday Nov 3, 6pm  7% of the voters. 3% of the votes.    3
Tuesday Nov 4, 6pm  2% of the voters. 1% of the votes.    1
Wednesday Nov 5, 6pm  5% of the voters. 2% of the votes.    2
Thursday Nov 6, 6pm  5% of the voters. 2% of the votes.    2
Friday Nov 7, 4pm  53% of the voters. 21% of the votes.    23
Saturday Nov 8, 10am  47% of the voters. 18% of the votes.    20
Sunday Nov 9, 7pm  30% of the voters. 12% of the votes.    13
Poll ended at 6:05 pm on Monday October 27th 2014. Total votes: 110. Total voters: 43.
Please choose the time slots that are the most convenient for you to have the midterm quiz. You can choose up to 3 options, but you don't have to: if 1 time slot is much better than the others for you, then choose only 1. Vote before Monday Oct. 27th, because we will then decide in class when the midterm will take place.
1.  The midterm quiz covers assignments 1-5
2.  Assignment #5 is due on October 29th.
3.  There is an aerospace department party on Nov. 1st in the afternoon
Fluid Mechanics Midterm Quiz
November 7th 2014
17:00 — 19:00

Question #1
Water is flowing in a horizontal pipe with a diameter of 50 mm into another pipe with a diameter of 70 mm. A Venturi meter is placed between these two pipes. A differential manometer shows a $72$ mm Hg difference in height. It is connected to the Venturi meter's narrowest cross section with a diameter of 35 mm, and to the inlet section with a diameter of 50 mm. Determine the mean velocity in the pipe with the diameter 70 mm.
Question #2
The model of a wind turbine (windmill) is to be tested in a low speed wind tunnel. The starting torque, and the power output at various angular velocities, are the dependent variables of specific interest. Determine suitable non-dimensional forms for these two parameters and the criteria of similarity on which they depend. Discuss what difficulties are likely to arise if dynamically-similar tests are made in a wind tunnel.

A 1/20$^{\rm th}$ scale model is tested in a tunnel and it is decided that the effects of viscosity will be unimportant. The model produces 50 W in a wind speed of 5 m/s when rotating at $240$ rpm. Determine the power output of the prototype when the angular velocity is 30 rpm under dynamically-similar conditions. What is the corresponding wind speed? The air density is the same for the model and the prototype.
Question #3
Consider water at rest in a container as follows:
figure3.png  ./download/file.php?id=2235&sid=7eeaf3b9866f7ca465dbd1a18a0ba9f4  ./download/file.php?id=2235&t=1&sid=7eeaf3b9866f7ca465dbd1a18a0ba9f4
Knowing that the air pressure inside the tank is of 2 atm, that the surrounding air pressure is equal to 1 atm, that the lever length $L=4$ m, and that $H_1=10$ m, $W_1=2$ m, $W_2=1.5$ m:
(a)  Find $H_2$ in meters
(b)  Find the force per unit depth $F$ (in Newtons per meter) needed to prevent the lever from rotating around the pivot A.
Question #4
Because of heavy rain, the Oncheon stream overflows near the PNU subway station. A large amount of mud lies in the streets and you are the engineer in charge of removing this mud. For this purpose, you use a truck on which a plow is mounted at the front, and use it to move the mud out of the road as follows:

figure4.png  ./download/file.php?id=2236&sid=7eeaf3b9866f7ca465dbd1a18a0ba9f4  ./download/file.php?id=2236&t=1&sid=7eeaf3b9866f7ca465dbd1a18a0ba9f4
Knowing that the truck travels at 30 km/hour, that the width of the mud $W$ is of 1 m, that the height of the mud $H$ is of 30 cm, that the density of the mud can be taken as 1700 kg/m$^3$, do the following:
(a)  Find the force necessary to push the plow.
(b)  Find the power necessary to push the plow.
Hint: You can neglect the friction force between the mud and the plow.
1.  1.21 m/s.
2.  $\Pi_1={\cal P}/\rho \omega^3 D^5$, $\Pi_2={\cal T}/\rho \omega^2 D^5$, $\Pi_3=\mu/\rho \omega D^2$, $\Pi_4=\omega D/q_\infty$; 312500 W; 12.5 m/s.
3.  20.34 m, 346 kN/m.
4.  64.4 kN, 536 kW.
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