Final answer:
The velocity in a 12-inch diameter pipe with a flow rate of 50 gal/min is 8.5 ft/min after converting the flow rate to cubic feet per minute and finding the cross-sectional area of the pipe.
Step-by-step explanation:
The question relates to the relationship between flow rate and velocity in a pipe system. To determine the velocity in a pipe, we use the formula Q = Av, where Q is the flow rate, A is the cross-sectional area of the pipe, and v is the velocity of the fluid. Given a flow rate of 50 gal/min and a diameter of 12 inches, we first convert gallons per minute to cubic feet per minute (since 1 gallon = 0.133681 cubic feet), and then find the cross-sectional area of the pipe in square feet. Once these conversions are complete, we can solve for velocity.
To calculate:
1. Convert the flow rate: 50 gal/min × 0.133681 ft³/gal = 6.68405 ft³/min
2. Calculate the area of the pipe (A = πr²):
- Radius (r) = ½ diameter (12 inches) = 6 inches = 0.5 ft
- A = π × (0.5 ft)² = 0.7854 sq ft
3. Solve for velocity (v = Q/A):
- v = 6.68405 ft³/min / 0.7854 sq ft = 8.5 ft/min
Therefore, the correct answer is a. 8.5 FT/MIN.