Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Continuity equation, kinematics and dynamics of flow
Question Statement:
A main distribution conduit carries a discharge of $0.180\text{ m}^3/\text{s}$ and splits into two identical parallel delivery branch pipes, each having an internal diameter of $200\text{ mm}$ ($0.20\text{ m}$). Assuming equal flow division between the two branches, the mean water velocity in each branch pipe in meters per second ($\text{m/s}$) is ________ (round off to two decimal places). Take $\pi = 3.1416$.
Answer Key:
2.86
Step-by-Step Solution & Explanation
1. Flow in each branch pipe:
$Q_1 = \frac{Q}{2} = \frac{0.180}{2} = 0.090\text{ m}^3/\text{s}$
2. Cross-sectional area of a branch pipe:
$A_1 = \frac{\pi}{4} D_1^2 = \frac{3.1416}{4} \times (0.20)^2 = 0.031416\text{ m}^2$
3. Mean flow velocity via continuity equation $Q_1 = A_1 V_1$:
$V_1 = \frac{Q_1}{A_1} = \frac{0.090}{0.031416} = 2.86478\text{ m/s} \approx 2.86\text{ m/s}$