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2. The tank shown is to be drained to a sewer. Determine the size of new Schedule 40 steel pipe that will carry at least 400 gal/min of water at 80 degree F through the system. The total length of the pipe is 75 ft.

User Loonis
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To determine the size of the new Schedule 40 steel pipe required to carry at least 400 gallons per minute (gpm) of water at 80 degrees Fahrenheit (F) through a system with a total length of 75 feet, we can use the Hazen-Williams equation. This equation relates the flow rate, pipe diameter, pipe length, and other factors.

The Hazen-Williams equation is as follows:

Q = 0.00254 * C * d^2 * (h^(0.63)) * (l^(0.54))

Where:

Q is the flow rate (gallons per minute)

C is the Hazen-Williams coefficient (dependent on the pipe material)

d is the pipe diameter (in inches)

h is the head loss (feet per 100 feet of pipe)

l is the pipe length (feet)

First, we need to determine the Hazen-Williams coefficient (C) for Schedule 40 steel pipe. The Hazen-Williams coefficient for Schedule 40 steel pipe is typically around 120.

Next, we can rearrange the Hazen-Williams equation to solve for the pipe diameter (d):

d = (Q / (0.00254 * C * (h^(0.63)) * (l^(0.54))))^(1/2)

Plugging in the given values:

Q = 400 gpm

C = 120

h = 0 (assuming no significant head loss)

l = 75 ft

d = (400 / (0.00254 * 120 * (0^(0.63)) * (75^(0.54))))^(1/2)

d = (400 / (0.00254 * 120 * 1 * 75^(0.54)))^(1/2)

Using a calculator, we can solve this equation:

d ≈ 3.56 inches

Therefore, a new Schedule 40 steel pipe with a diameter of approximately 3.56 inches would be needed to carry at least 400 gallons per minute of water at 80 degrees Fahrenheit through a 75-foot system with no significant head loss.

User Henrik Fransas
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