Final answer:
c. 1.77. To find the water velocity, we first convert the flow rate from gpd to fps using a conversion factor. Then, we calculate the cross-sectional area of the force main using the formula for the area of a circle. Finally, we use the flow rate and cross-sectional area to calculate the water velocity. The correct answer is approximately 1.77 fps.
Step-by-step explanation:
To find the water velocity, we first need to convert the flow rate from gallons per day (gpd) to cubic feet per second (fps). There are 7.48 gallons in 1 cubic foot and 24 hours in a day, so the conversion factor is:
1 gpd = 7.48 / 24 / 60 / 60 fps
Once we have the flow rate in fps, we can calculate the water velocity. The velocity can be calculated using the equation:
Velocity = Flow rate / Cross-sectional area
The cross-sectional area can be calculated using the formula:
Area = π * (diameter/2)^2
Substituting the values into the equation, we can calculate the water velocity:
Velocity = Flow rate / Area
Plugging in the values, we get:
Velocity = 400,000 / (π * (8/2)^2)
Calculating this gives us a velocity of approximately 1.78 fps, which is closest to option (c) 1.77.