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What is the rate of flow in liters per second in a 300mm diameter pipe with a water velocity of 0.8 m/s?
48 L/s
57 L/s
60 L/s
75 L/s
The correct answer is: 57 L/s
To determine the rate of flow in liters per second in a pipe, you can use the formula for flow rate, which is the product of the cross-sectional area of the pipe and the velocity of the fluid. First, calculate the cross-sectional area of the pipe. The formula for the area \( A \) of a circle is: \[ A = \pi r^2 \] Given that the diameter of the pipe is 300 mm, the radius \( r \) is half of that: \[ r = \frac{300mm}{2} = 150mm = 0.15m \] Now, plug the radius into the area formula: \[ A = \pi (0.15m)^2 \approx \pi \times 0.0225 m^2 \approx 0.0707 m^2 \] Next, multiply the area by the velocity to find the flow rate \( Q \): \[ Q = A \times velocity = 0.0707 m^2 \times 0.8 m/s \approx 0.05656 m^3/s \] Since 1 cubic meter equals 1000 liters, you convert cubic meters to liters: \[ Q \approx 0.