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.