Problem Statement:
Water is pumped from a large tank shown in the figure. The friction loss for the pipe is given as hf = 5 m, and the velocity of the flow inside the pipe is V = 4.7 m/s. Ignoring minor losses, find the required pump power. The density of water is 1000 kg/m3, and the pressure at both locations (1) and (2) is atmospheric.
Given:
- Pipe area: 0.01 m2
- Friction loss: hf = 5 m
- Flow velocity: V = 4.7 m/s
- Density of water: 1000 kg/m3
- Pressure at locations (1) and (2): Atmospheric
Find:
Required pump power (Wnet).
Pump Power Calculation
Step 1: Determine the Flow Rate
The flow rate (Q) can be calculated using the velocity (V) and the cross-sectional area (A) of the pipe:
Q = A × V
Given:
A = 0.01 m2, V = 4.7 m/s
Therefore:
Q = 0.01 m2 × 4.7 m/s = 0.047 m3/s
Step 2: Calculate the Head Loss Due to Friction
The head loss (hf) is given as 5 meters.
Step 3: Calculate the Pump Power
The pump power (Wnet) can be calculated using the formula:
Wnet = ρ × g × Q × hf
Where:
- ρ is the density of water (1000 kg/m3)
- g is the acceleration due to gravity (9.81 m/s2)
- Q is the flow rate (0.047 m3/s)
- hf is the head loss (5 m)
Plugging in the values:
Wnet = 1000 kg/m3 × 9.81 m/s2 × 0.047 m3/s × 5 m
Step 4: Perform the Calculation
Wnet = 1000 × 9.81 × 0.047 × 5
Wnet = 2307.15 W
Conclusion
Therefore, the required pump power is 2307.15 W.
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