Me 3560 class problems 4 PDF

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At a sudden contraction in a pipe the diameter changes from 1 to 2. The pressure drop,  , which develops across the contraction is a function of 1 and 2, as well as the velocity, , in the larger pipe, and the fluid density, , and viscosity, . Use 1, , and  as repeating variables to determine a suitable set of dimensionless parameters. Why would it be incorrect to include the velocity in the smaller pipe as an additional variable?

A thin elastic wire is placed between rigid supports. A fluid flows past the wire, and it is desired to study the static deflection, δ, at the center of the wire due to the fluid drag. Assume that: (, , , , )

where is the wire length,

the wire diameter, the fluid density,  the fluid viscosity,

the fluid velocity, and

the modulus of elasticity of the wire material. Develop a suitable set of pi terms for this problem.

The drag characteristics for a newly designed automobile having a maximum characteristic length of 20 ft are to be determined through a model study. The characteristics at both low speed (approximately 20 mph) and high speed (90 mph) are of interest. For a series of projected model tests, an unpressurized wind tunnel that will accommodate a model with a maximum characteristic length of 4 ft is to be used. Determine the range of air velocities that would be required for the wind tunnel if Reynolds number similarity is desired. Are the velocities suitable? Explain.

0 sin ω , where is the velocity) with a frequency An incompressible fluid oscillates harmonically ( = V of 10 rad/s in a 4-in.-diameter pipe. A ¼ scale model is to be used to determine the pressure difference per unit length,  ℓ (at any instant) along the pipe. Assume that

where is the pipe diameter, ω the frequency, the time,  the fluid viscosity, and the fluid density. If the same fluid is Determine the similarity requirements for the model and the prediction equation for  ℓ. used in the model and the prototype, at what frequency should the model operate?

Glycerin at 20 °C flows upward in a vertical 75-mm-diameter pipe with a centerline velocity of 1.0 m/s. Determine the head loss and pressure drop in a 10-m length of the pipe.

Water flows through a horizontal plastic pipe with a diameter of 0.2 m at a velocity of 10 cm/s. Determine the pressure drop per meter of pipe using the Moody chart.

Water at 10 °C is pumped from a lake as shown. If the flowrate is 0.011 m3/s, what is the maximum length inlet pipe, , that can be used without cavitation occurring?

o a . Water at 10 C flows from -2 large reservoir at the rate of 1.5 ×10 m3/s through the system shown. Determine the pressure at .

For the system shown, calculate the vertical distance between the surfaces of the two reservoirs when water at 10 oC flows 3 from to at the rate of 0.03 m /s. The elbows are standard. The total length of the 3-in pipe length is 100 m. For the 6-in pipe it is 300 m.

o Kerosene at 25 C is flowing in the system shown. The total length of the 2–in copper pipe is 30 m. The two 90o elbows have a radius of 300 mm. Determine the volume flow rate into tank if a pressure of 150 kPa is maintained above the kerosene in tank .

3 o What is size of standard copper tube is required to transfer 0.06 m/s of water at 80 C from a heater where the pressure is 150 kPa to an open tank. The water flows from the end of the tube into the atmosphere. The pipe is horizontal and 30 m long....