.75m pipe connects two reservoirs. water is pumped from the lower reservoir to a reservoir 42m higher using a 850 kw pump, ep=78%. If Head losses are 22m, draw EGL/ HGL
To draw the Energy Grade Line (EGL) and Hydraulic Grade Line (HGL) for this system, we need to consider the energy changes and head losses between the two reservoirs.
1. Calculate the total head difference:
The total head difference between the two reservoirs can be calculated by subtracting the head loss from the elevation difference.
Elevation difference = 42 m
Head loss = 22 m
Total head difference = Elevation difference + Head loss
Total head difference = 42 m + 22 m = 64 m
2. Calculate the discharge:
Since we have the power and efficiency of the pump, we can find the discharge using the formula:
Discharge (Q) = Power (P) / (ρ * g * H * efficiency)
Where:
ρ = density of the fluid (we'll assume water) = 1000 kg/m^3
g = acceleration due to gravity = 9.81 m/s^2
H = total head difference = 64 m
efficiency = 0.78 (or 78% expressed as a decimal)
Substituting the given values:
Discharge (Q) = 850,000 W / (1000 kg/m^3 * 9.81 m/s^2 * 64 m * 0.78)
Discharge (Q) ≈ 18.72 m^3/s
3. Calculate the velocity:
The velocity of the fluid can be found using the discharge and the cross-sectional area of the pipe.
Cross-sectional area = (π * diameter^2) / 4
Since the diameter of the pipe is not given, we proceed using a generic pipe diameter to find the velocity.
Assume a pipe diameter of 1 m:
Cross-sectional area = (π * 1^2) / 4 = 0.785 m^2
Velocity (V) = Discharge (Q) / Cross-sectional area
Velocity (V) = 18.72 m^3/s / 0.785 m^2 ≈ 23.84 m/s
4. Plotting the EGL and HGL:
To draw the EGL and HGL, we start from the lower reservoir and consider the energy changes and head losses as we move towards the higher reservoir.
- EGL (Energy Grade Line):
Start by drawing a horizontal line at the energy level of the lower reservoir (0 m). Then, plot points corresponding to the increase in the total head difference (64 m) and the pump work done (850 kWh). Connect these points with a line to represent the change in energy.
- HGL (Hydraulic Grade Line):
Start at the same point where the EGL started (0 m) and draw a horizontal line. Then, plot points corresponding to the elevation changes (42 m) and the head losses (22 m). Connect these points with a line to represent the change in hydraulic head.
The EGL and HGL lines will have the same starting point but may differ in slope due to the various energy changes and head losses.
Note: It is important to note that the specific pipe diameter was not provided, so the velocity, cross-sectional area, and hence the EGL and HGL slopes would vary depending on the actual pipe diameter.