1. A gas flowing through a horizontal pipe at a steady velocity. A water manomet

Question

1. A gas flowing through a horizontal pipe at a steady velocity. A water manometer is used to measure the flow.

a. Write an expression for the pressure difference between points A and B in terms of Y and the density of water.

b. Assume the weight density of water is 62 lbs/ft^3 and that Y is 3 inches. What is the pressure difference between B and A in lbs/ft^2 ? What about in psi?

2. Consider the following well drilled 7000 feet vertically with a (essentially) horizontal leg of 700 feet length. The entire well is cased (closed) except for a one foot long cylindrical region at the end of the horizontal leg. The vertical section is 8 inches in diameter, the horizontal leg 4 inches in diameter. At the top of the well there is a valve and pressure meter.

The above well has been shut-in (valve closed) for several months. At this point the pressure gauge reads 570 psia. Assume the weight density of the oil in the well is 50 lbs/ft^3 and that the well is filled with oil. What is the pressure at point A (the entrance to the well)?

3. Consider a tall vertical cylindrical container of height "H" at atmospheric pressure. A precisely fitted plug is dropped into the cylinder and falls--compressing the air. After a brief period of oscillation the plug settles to a height "h." Assume the air behaves as an ideal gas and all this takes place at constant temperature.

a. Write an expression for the new value of the pressure in the cylinder as a function of "H" and "h."

b. Assuming h=H/2 and that the radius of the cylinder is 5 inches, what is the weight of the plug?

Explanation / Answer

1)

a)

Pa - Pb = rho_w*y......where rho_w = density of water

b)

Pa - Pb = 62*(3/12)

Pa - Pb = 15.5 lb/ft^2

Pa - Pb = 15.5 / 12^2 psi

Pa - Pb = 0.1076 psi

2.

Pressure = P + rho*h

P = 570 + 50*7000 / 12^2

P = 3000.55 psi

3.

a)

Volume V1 = (pi/4)*d^2 * H

Volume V2 = (pi/4)*d^2 *h

V1 / V2 = H / h

For constant temperature process, P2 / P1 = V1 / V2

Hence, P2 / P_atm = H / h

P2 = P_atm*(H / h)

b)

h = H/2

P2 = P_atm*H / (H/2)

P2 = 2*P_atm

Also, P2 = P_atm + pressure due to weight

P2 = P_atm + Weight / area

2*P_atm = P_atm + Weght / (pi*r^2)

P_atm = Weight / (3.14*5^2)

Assuming P_atm = 14.7 psi

14.7 = Weight / (3.14*5^2)

Weight = 1153.95 lb

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