Final answer:
Option D). The relationship between carrying capacity and flow rate in a pipe can be understood using the equation 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. As the cross-sectional area of the pipe increases, the flow rate increases, assuming the velocity remains constant. Similarly, if the cross-sectional area increases and the flow rate is held constant, the velocity of the fluid will decrease.
Step-by-step explanation:
The equation Q = Av, where Q is the flow rate, A is the pipe's cross-sectional area, and v is the fluid's velocity, can be used to understand the relationship between carrying capacity and flow rate in a pipe. Assuming the velocity stays constant, the flow rate increases as the pipe's cross-sectional area grows. In a similar vein, the fluid's velocity will drop if the cross-sectional area grows while the flow rate remains constant.
In the given question, we need to find the velocity in a pipe with a flow rate of 50 gal/min and a diameter of 4 inches. First, we convert the flow rate from gallons to cubic feet, and then we calculate the cross-sectional area of the pipe using the diameter. Finally, we can use the equation Q = Av to find the velocity.
The correct answer is d. 79 FT/MIN.