ES 65 ProbleES 65 ProbleES 65 ProbleES 65 Problemmmm Drill IIDrill IIDrill IIDrill II

1. A fluid flows through two horizontal pipes of equal length which are connected together to form a pipe of

length 2222LLLL.... The flow is laminar and fully developed. The pressure drop for the first pipe is 1.44 times greater

than it is for the second pipe. If the diameter of the first pipe is DDDD, determine the diameter of the second pipe.

Answer: 1.095DAnswer: 1.095DAnswer: 1.095DAnswer: 1.095D

2. A manufacturer makes two types of drinking straws: one with a square cross-sectional shape, and the other

type the typical round shape. The amount of material in each straw is to be the same. That is, the length of

the perimeter of the cross section of each shape is the same. For a given pressure drop, what is the ratio of

the flowrates through the straws? Assume the drink is viscous enough to ensure laminar flow and neglect

gravity.

3. The velocity profile in a circular pipe can be determined as shown in Figure. Air at a temperature of 83 °F

and an absolute pressure of 29.1 in. of mercury is supplied at a constant flowrate through the pipe.

According to a flowmeter on the device, the flowrate is Q = 0.671 cfs. A Pitot tube used to determine the air

speed is connected to a water-filled manometer and can be positioned at various locations across the

diameter of the pipe at the outlet. Experimentally determined values of the manometer reading, h, as a

function of the radial distance from the pipe center, r, are shown in the following table. Use these results to

plot a graph of the air speed, u, as a function of the radial distance, r.

The flowrate associated with an axisymmetric velocity profile in a pipe can he determined from

velocity profile data by

Q= 2� � �����/�

Use the calculated u as a function of r data to

determine Q. Note: Some type of numerical or

graphical integration of the experimental data is

needed.

Compare your experimentally determined

flowrate with that given by the flowmeter listed above.

Discuss some possible reasons for any difference

between the two values.

4. If 140 L/s of oil flows through the system shown,

determine the total head lost between points B and C.

Ans: 11.8 mAns: 11.8 mAns: 11.8 mAns: 11.8 m

5. The flow rate of water through a cast iron pipe is 5000 GPM. The diameter of the pipe is 330 mm, and the

coefficient of friction is f= 0.0173. What is the pressure drop over a 30-rn length of pipe? Ans: 10.72 kPaAns: 10.72 kPaAns: 10.72 kPaAns: 10.72 kPa

6. The water system in a suburban area consists of an old 200-mm pipeline 760 m long which conveys water from a

pump to a reservoir whose water surface is 107 m higher than the pump. Water is pumped at the rate of 0.07 m3/s.

Determine the horsepower saved by replacing the old pipe with a new 250 - mm pipe. Assume the value of f as

equal to 0.033 and 0.022, respectively, for the old and new pipes. Neglect losses of head except friction head.

Ans: 22Ans: 22Ans: 22Ans: 22....82 hp82 hp82 hp82 hp

7. Derive the kinetic energy head of a fully developed laminar flow which has a parabolic velocity distribution profile

and having an average velocity v. Ans: K.E head = Ans: K.E head = Ans: K.E head = Ans: K.E head = ½½½½ VVVV2222/2g/2g/2g/2g

8. A pipe network consists of pipeline 1 from A to B, then at B it is connected to pipelines 2 and 3, where it merges

again at Joint C to form a single pipeline 4 up to point D. Pipelines 1, 2 and 4 are in series connection whereas

pipelines 2 and 3 are parallel to each other. If the rate of flow from A to B is 10 liters/sec and assuming f = 0.02

for all pipes, Determine the flow in each pipe and the total head lost from A to D.