Question

A nuclear power plant draws 3.1×106 L/min of cooling water from the ocean.

If the water is drawn in through two parallel, 3.4-m-diameter pipes, what is the water speed in each pipe?

Answer 1

Main Answer:

The water speed in each pipe is approximately 4.78 m/s.

Step-by-step explanation:

To find the water speed, we can use the formula for volume flow rate, which is given by Q = A * v, where Q is the flow rate, A is the cross-sectional area, and v is the velocity of the fluid. Rearranging the formula to solve for velocity, we get v = Q / A. Given the volume flow rate of 3.1×10^6 L/min and two parallel pipes with a total diameter of 3.4 meters, the area can be calculated using the formula for the area of a circle, A = π * (diameter/2)^2.

Hence, A = π *
`(3.4/2)^2 = π * 1.7^2 = π * 2.89 ≈ 9.07`m² for each pipe. Converting the flow rate from liters per minute to cubic meters per second by dividing by 1000 and 60, we get 3.1×10^6 L/min ≈ 51,667 L/s ≈ 0.05167 m³/s for each pipe. Substituting the values into the formula v = Q / A, we find the velocity for each pipe: v = 0.05167 m³/s / 9.07 m² ≈ 4.78 m/s.

Therefore, the water speed in each pipe is approximately 4.78 m/s.

Answer 2

The water speed in each pipe is approximately 2.10 m/s.

Step-by-step explanation:

To find the water speed in each pipe, we can use the principle of continuity, which states that the volume flow rate at any point in a pipe must be constant if the pipe is incompressible and has steady flow. The volume flow rate is given by Q = A * V, where Q is the flow rate, A is the cross-sectional area of the pipe, and V is the velocity of the water.

Given that the nuclear power plant draws 3.1×106 L/min of cooling water from the ocean, and the water is drawn in through two parallel, 3.4-m-diameter pipes, we can calculate the flow rate in each pipe:

Flow rate in each pipe = Total flow rate / Number of pipes = (3.1×106 L/min) / 2 = 1.55×106 L/min

Converting the flow rate to m3/s:

Flow rate in each pipe = (1.55×106 L/min) * (1 min / 60 s) * (1 m3 / 1000 L)

Now, we can use the formula for the volume flow rate to find the water speed in each pipe:

Flow rate = A * V

Solving for V:

V = Flow rate / A

Substituting the values:

V = (1.55×106 L/min) * (1 min / 60 s) * (1 m3 / 1000 L) / [(3.4 m / 2)2 * π]

Calculating the value:

V ≈ 2.10 m/s

Therefore, the water speed in each pipe is approximately 2.10 m/s.