Question

Estimate the friction losses of 50 m long PVC pipe having inside diameter 50 mm. The velocity of flowing water is 1.0 m/s and friction factor of pipe is 0.05.

• A. 10.20 m
• B. 2.54 m
• C. 3.1 m
• D. 1.52 m

Hint:

Always ensure all units are in standard SI form before substituting into the Darcy-Weisbach equation (e.g., converting the diameter from $50 \text{ mm}$ to $0.05 \text{ m}$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Friction loss ($h_f$) in a pressurized pipe flow is calculated using the Darcy-Weisbach equation.
Key Formula or Approach:
The Darcy-Weisbach equation is:
\[ h_f = \frac{f \cdot L \cdot v^2}{2 \cdot g \cdot D} \] where:
- $f$ is the dimensionless pipe friction factor.
- $L$ is the length of the pipe (m).
- $v$ is the velocity of the water (m/s).
- $D$ is the inside diameter of the pipe (m).
- $g$ is the acceleration due to gravity ($9.81 \text{ m/s}^2$).

Step 2: Detailed Explanation:
Given values:
- Pipe length ($L$) = $50 \text{ m}$
- Inside diameter ($D$) = $50 \text{ mm} = 0.05 \text{ m}$
- Flow velocity ($v$) = $1.0 \text{ m/s}$
- Friction factor ($f$) = $0.05$
- Acceleration due to gravity ($g$) = $9.81 \text{ m/s}^2$
Substitute these values into the Darcy-Weisbach equation:
\[ h_f = \frac{0.05 \times 50 \times (1.0)^2}{2 \times 9.81 \times 0.05} \] Since the friction factor $f$ and diameter $D$ are both $0.05$, they cancel out:
\[ h_f = \frac{50 \times 1.0}{2 \times 9.81} = \frac{50}{19.62} \approx 2.548 \text{ m} \] This is approximately ______2.54 m______.

Step 3: Final Answer:
The friction loss in the PVC pipe is 2.54 m, corresponding to option (B).