Question

Compute the head loss due to friction in a pipe 7.5 cm in diameter and 120 m long when the water is flowing at a velocity of 1.8 m/s. The value of f may be assumed to be 0.005:

• A. 4 m
• B. 4.32 m
• C. 5.28 m
• D. 6 m

Hint:

Note whether the given value \(f\) represents the "friction factor" or the "coefficient of friction".
The standard coefficient of friction requires the factor of 4 in the numerator (\(4f\)), while the friction factor (\(f'\)) is \(4f\).
Here, using \(4f\) yields the exact target option of 5.28 m.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Frictional resistance along a pipe wall causes a continuous drop in pressure head as fluid flows through it, which is modeled using the Darcy-Weisbach equation.

Step 2: Key Formula or Approach:
The Darcy-Weisbach equation for head loss (\(h_f\)) is:
\[ h_f = \frac{4 f L v^2}{2 g d} \] where:
\(f\) = coefficient of friction (given as \(0.005\))
\(L\) = length of pipe (\(120\text{ m}\))
\(v\) = fluid velocity (\(1.8\text{ m/s}\))
\(d\) = pipe diameter (\(7.5\text{ cm} = 0.075\text{ m}\))
\(g\) = acceleration due to gravity (\(9.81\text{ m/s}^2\))

Step 3: Detailed Explanation:
Substitute the given values into the equation:
\[ h_f = \frac{4 \times 0.005 \times 120 \times (1.8)^2}{2 \times 9.81 \times 0.075} \] First, simplify the terms in the numerator:
\[ \text{Numerator} = 0.02 \times 120 \times 3.24 = 2.4 \times 3.24 = 7.776 \] Next, simplify the terms in the denominator:
\[ \text{Denominator} = 19.62 \times 0.075 = 1.4715 \] Now, calculate the friction head loss \(h_f\):
\[ h_f = \frac{7.776}{1.4715} \approx 5.284\text{ m} \approx 5.28\text{ m} \]

Step 4: Final Answer:
The correct option is 3, which corresponds to 5.28 m.