To calculate the Flow Rate (Q) in a partially filled pipe:
\[ Q = \frac{r^2}{2} \left( \theta - \sin(\theta) \right) \]
Where:
Partial pipe flow occurs when a pipe is not completely full of fluid, and the flow rate is determined by the cross-sectional area of the fluid in the pipe. This situation is common in sewer systems and open channel flows where the pipe is not under pressure and the fluid is subject to gravity. The flow rate is influenced by the shape of the pipe, the roughness of the pipe’s interior, and the slope of the pipe.
Let's assume the following values:
Using the formula:
\[ Q = \frac{12^2}{2} \left( 1.5 - \sin(1.5) \right) = \frac{144}{2} \left( 1.5 - 0.9975 \right) = 72 \times 0.5025 = 36.18 \text{ cubic feet per second} \]
The flow rate is approximately 36.18 cubic feet per second.
