Question
Download Solution PDFWater is flowing through a pipe of diameter 15 cm. At a section, the gauge pressure is 40 kPa and mean velocity is found to be 2 m/s. If the centerline of the pipe is 10 m above the datum, the total head in the flow will be given by
[Kinetic energy correction factor = 1.2, g = 10 m/s²]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The total head in a flow is given by the extended Bernoulli equation including the kinetic energy correction factor:
\( H = \frac{p}{\gamma} + \alpha \frac{V^2}{2g} + z \)
Given:
- Gauge pressure, \( p = 40~\text{kPa} = 40000~\text{N/m}^2 \)
- Mean velocity, \( V = 2~\text{m/s} \)
- Elevation, \( z = 10~\text{m} \)
- Kinetic energy correction factor, \( \alpha = 1.2 \)
- Specific weight of water, \( \gamma = 1000 \times 10 = 10000~\text{N/m}^3 \)
Calculation:
\( \frac{p}{\gamma} = \frac{40000}{10000} = 4~\text{m} \)
\( \alpha \times \frac{V^2}{2g} = 1.2 \times \frac{4}{20} = 0.24~\text{m} \)
\( z = 10~\text{m} \)
Total Head:
\( H = 4 + 0.24 + 10 = 14.24~\text{m}\)
Last updated on Jul 1, 2025
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