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.