How many cubic feet of nitrogen are needed to raise the pressure in an 8 inch diameter pipe 400 feet long to 20 psi?

Answer 1

To calculate the amount of nitrogen gas required to raise the pressure in a pipe, we need to follow these steps:

1.	Calculate the volume of the pipe in cubic feet.

2.	Apply the Ideal Gas Law to determine how much nitrogen is needed to achieve the desired pressure.

Step 1: Calculate the Volume of the Pipe

The formula for the volume of a cylinder (which is the shape of the pipe) is:

V = \pi \times r^2 \times h

where:

•	 r  is the radius of the pipe (half the diameter),

•	 h  is the length of the pipe.

Given:

•	Diameter of the pipe,  d = 8  inches,

•	Length of the pipe,  h = 400  feet.

First, convert the diameter to feet:

d = \frac{8 \text{ inches}}{12 \text{ inches per foot}} = 0.6667 \text{ feet}

The radius r is half of that:

r = \frac{0.6667}{2} = 0.3333 \text{ feet}

Now, calculate the volume:

V = \pi \times (0.3333)^2 \times 400 \approx 139.3 \text{ cubic feet}

Step 2: Apply the Ideal Gas Law

The Ideal Gas Law in terms of volume and pressure is:

PV = nRT

Where:

•	 P  is the pressure,

•	 V  is the volume,

•	 n  is the amount of gas (in moles),

•	 R  is the ideal gas constant,

•	 T  is the temperature.

To find the additional volume of nitrogen required to increase the pressure to 20 psi, we’ll compare the initial and final states of the gas assuming temperature and the amount of gas are constant.

Using the relationship between pressure and volume at constant temperature and gas amount:

\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}

Since temperature T and n (number of moles) are constant, we can simplify it to:

P_1 \times V_1 = P_2 \times V_2

Assuming the initial pressure P_1 is 0 psi (no pressure), the entire volume of the pipe must be filled with nitrogen at the final pressure of 20 psi. Hence, the amount of nitrogen required is equal to the pipe’s volume at that pressure.

Thus, 139.3 cubic feet of nitrogen gas is required to raise the pressure in the pipe to 20 psi, assuming no initial pressure.

Answer 2

47,298 SCF