What are the factors that contribute to the total dynamic discharge head in a pump system?
The total dynamic discharge head is 280.06 kPa. To calculate the total dynamic discharge head, we need to consider the pressure difference, elevation difference, and velocity head in both the suction and discharge lines.
Calculating Total Dynamic Discharge Head
To calculate the total dynamic discharge head, we need to consider various factors that contribute to the overall head loss in the pump system. These factors include pressure differences, elevation changes, and velocity heads in the suction and discharge lines.
Pressure Difference in Suction Line:
The pressure at the suction point is 178.5 kPa. As the tank is closed, there is no pressure loss due to elevation. Therefore, the pressure difference in the suction line is calculated as:
Pressure difference in suction line = Pressure at suction point - Pressure at pump suction
= 178.5 kPa - 0 kPa
= 178.5 kPa
Pressure Difference in Discharge Line:
The pressure at the discharge point is 194.91 kPa, and the elevation difference is 9.6 m. Converting the elevation difference to pressure using the specific gravity (sg) of the liquid, we get the pressure due to elevation as:
Pressure due to elevation = Elevation difference * sg * g
= 9.6 m * 0.981 * 9.81 m/s^2
= 93.84 kPa
Therefore, the pressure difference in the discharge line is:
Pressure difference in discharge line = Pressure at discharge point - Pressure due to elevation
= 194.91 kPa - 93.84 kPa
= 101.07 kPa
Velocity Head:
The velocity head in both the suction and discharge lines can be calculated using the equation:
Velocity head = (Velocity^2) / (2 * g)
For the suction line with a velocity of 2.8 m/s and friction loss of 1.3 m:
Velocity head in suction line = ((2.8 m/s)^2) / (2 * 9.81 m/s^2)
= 0.40 m
For the discharge line with a velocity of 3.4 m/s and friction loss of 3.9 m:
Velocity head in discharge line = ((3.4 m/s)^2) / (2 * 9.81 m/s^2)
= 0.59 m
Total Dynamic Discharge Head:
Finally, the total dynamic discharge head is calculated by summing up the pressure differences and velocity heads in both the suction and discharge lines:
Total dynamic discharge head = Pressure difference in suction line + Pressure difference in discharge line + Velocity head in suction line + Velocity head in discharge line
= 178.5 kPa + 101.07 kPa + 0.40 m + 0.59 m
= 280.06 kPa
Therefore, the total dynamic discharge head in this pump system is 280.06 kPa, taking into account the various factors that contribute to the overall head loss.