# Calculation of Discharge in a Pipe ## Given Data - Diameter of the pipe, \( D = .15\, \text{m} \) - Velocity of water, \( v = 2.5\, \text{m/s} \) ## Step 1: Find the cross-sectional area of the pipe The cross-sectional area \(A\) of a circular pipe is given by: \[ A = \frac{\pi}{4} D^2 \] Substitute \( D = .15\, \text{m} \): \[ A = \frac{\pi}{4} \times (.15)^2 \] \[ A = \frac{\pi}{4} \times .0225 \] \[ A \approx .7854 \times .0225 \approx .0177\, \text{m}^2 \] ## Step 2: Calculate the volumetric flow rate (discharge) Discharge \(Q\) is given by: \[ Q = A \times v \] \[ Q = .0177\, \text{m}^2 \times 2.5\, \text{m/s} = .04425\, \text{m}^3/\text{s} \] ## Step 3: Convert cubic meters per second to liters per second Since \(1\, \text{m}^3 = 100\, \text{L}\): \[ Q = .04425\, \text{m}^3/\text{s} \times 100\, \text{L/m}^3 = 44.25\, \text{L/s} \] ## **Final Answer:** \[ \boxed{ \text{Discharge} \approx \mathbf{44.25\, \text{L/s}} } \]