Reflection on Water Flow Rate Calculation
When analyzing the flow rate of water in a constricted pipe system, we can use the principle of continuity to determine the rate at which water flows through the system. The flow rate is calculated based on the pressure difference between two points and the geometry of the pipe system.
In the given scenario, a water pipe of diameter 10 inches constricts to a throat diameter of 5 inches. The water pressure in the pipe is 8 pounds per square inch, and in the throat, it is 6 pounds per square inch. To calculate the flow rate of water in cubic feet per second, we can use the formula:
Q = A1A2 * (sqrt(ΔP)/sqrt(ρ)) / sqrt(A12 - A22)
Where:
- Q is the flow rate
- A1 is the area of the pipe
- A2 is the area of the throat
- ΔP is the pressure difference
- ρ is the density of water
Given the diameter of the pipe and throat, as well as the pressures, we can substitute the values into the formula to calculate the flow rate.
Given that:
- Diameter of pipe = 10 in
- Diameter of throat = 5 in
- Pressure in the pipe = 8 psi
- Pressure in the throat = 6 psi
- Density of water (ρ) = 0.036 lb/in3
We can calculate the areas A1 and A2 using the formulas:
- A1 = π/4 * (10)2 in2 = 78.53 in2
- A2 = π/4 * (5)2 in2 = 19.63 in2
Substitute these values into the flow rate formula, we get:
Q = 78.53 * 19.63 * (sqrt(2) / sqrt(0.036)) / sqrt(78.532 - 19.632)
Q = 151.11 in3/s
Q = 12.59 ft3/s
Therefore, the flow rate of water in the constricted pipe system is 12.59 cubic feet per second.