Part I: Conceptual Questions

1 a. One set of basic dimensions is mass M, length L, and time T. For this system, the dimensions of force F are:

a. M

b. MLT-1

c. MLT-2

d. MT2 L-1

1 b. A two-dimensional gate is submerged in water. Circle the letter of the figure that best represents the pressure distribution of the water on the left hand (water) side of the gate.

A B C D E
1 c. Water flows without friction through the horizontal circular pipe having a varying cross sectional area as shown below. The velocity vectors indicate the magnitude and direction of the velocity. Please circle the figure that best describes the exit velocity profile based on the given inlet flow.

1 d. Water flows into a tank and flows out two exits to maintain a constant level in the tank, as shown in the figure below. The tank is sitting on a frictionless surface, so there is no contribution of force from the base, and there are no frictional losses from the flow. For this condition, determine the mass flow rate of the water being discharged through Port B:

Port A A A = 1500 mm 2

Port B A B = 1000 mm 2

_____________________________

1 e. [4 pts] Please circle the correct statement(s) associated with the major head loss, hL major and the minor head loss, hL minor of pipe line systems, etc.

a. hL major is always larger than hL minor

b. hL major is always smaller than hL minor

c. The values of hL major and hL minor depend on the specific features of each case. There is no such statement that is always hL major larger or smaller than hL minor

d. None of above

1 f. [5 pts] Lubrication oil flows at an average velocity of 20 m/s through a pipe line with a diameter of 0.40 m. The (absolute) roughness of this pipe e is 0.002 m . The absolute viscosity and density of this oil are 0.40 N s/m2 and 900 kg/m3 respectively. Please find the friction factor and mark this point in the Moody chart attached.

Part II: Problems

Problem 1: [ 20 points ] The drag force on a prototype sports car is to be determined experimentally using a “tow tank” which is a way of testing using water instead of air as the fluid.

The model length scale is 1/5 that of the prototype car. It is determined that

the drag force, FD, is a function of the Reynolds number based on length of the model, l,

as shown below:

Determine:

a) [10 pts] The speed the model is to be tested at if the prototype speed is 81 m/s

(180 mph).

b) [10 pts] The drag force on the prototype if the test model force is 182 N at this

speed.

Problem 2: [30pts] Water flows from a water tank through a piping system as shown below. The piping is smooth walled with a relative roughness of zero. The flow is assumed to be turbulent (fully developed).

The diameter of the piping is 6 inches and the length of the straight sections of pipe total 140 feet in length. At the end of the piping is a nozzle which has a 3 inch diameter discharge nozzle.

K elbow = 1.5 K valve = 5.0 K entrance = 0.2 K discharge nozzle = 0.5 based on entrance velocity  = 62.4 lbs/ft 3 6 inch pipe 60 feet 3 inch discharge nozzle

What is the velocity and corresponding flowrate through the piping system in cubic feet per minute?

V = __________________ ft/ s [25] Q = __________________ ft3/s [5]

Problem 3: [20 pts] An airplane is flying along at 280 mph or 412 ft/s. It is proposed that a large communications antenna be added to the roof of the fuselage. The antenna is a “blade” type antenna which extends outward 14 inches. It has a thickness, D of 1.0 inch and a chord length, l of 3.0 inches, or a fineness ratio of 3.

Please refer to the CD plot shown below to determine the correct drag coefficient. A sketch of the antenna is shown below. Use 0.002378 sl/ft3 for the density of air.

AntennaC:\Users\User\Desktop\14-34.jpg

a) [15] What is the drag force caused by the addition of the antenna?

D = _________________lbs

b) [5] How much extra HP is required to “drag” the antennae through the air at 280 mph?

HP = _________________

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