A pipe of 30 cm diameter carries water at a velocity of 20 m/s. At a point A on the pipe, measured pressure and elevation is 360 kN/m2 and 30.5 m. What is the pressure head at A.? (g = 10 m/s2)

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  1. 76.5 m
  2. 86.5 m
  3. 65.5 m
  4. 50.5 m

Answer (Detailed Solution Below)

Option 4 : 50.5 m
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Explanation:

To calculate the pressure head at point A, we need to consider both the elevation head and the velocity head. The pressure head can be calculated using the following formula:

\(\text{Pressure Head (H)} = \text{Elevation Head (h)} + \text{Velocity Head (h}_v\text{)} \)

Elevation Head (h):

The elevation head is the height of point A above a reference point. In this case, the elevation is given as 30.5 meters. So, the elevation head is:

Elevation Head (h)=30.5m

Velocity Head (hv):
The velocity head represents the energy associated with the motion of the fluid. It can be calculated using the formula:

\(\text{Velocity Head (h}_v\text{)} = \frac{v^2}{2g} \)

where:

\(v\) is the velocity of the fluid,

\(g\) is the acceleration due to gravity.

Given that the velocity of water is 20 m/s,

\(\text{Velocity Head (h}_v\text{)} = \frac{(20)^2}{2 \times 10} = 20 \, \text{m} \)

Pressure Head (H):

Finally, the pressure head is calculated by adding the elevation head and the velocity head:

Pressure Head (H)=Elevation Head (h)+Velocity Head (hv)

Pressure Head (H)=30.5m+20m=50.5m

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