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Definition: This calculator computes the water horsepower (\( P_{whp} \)) imparted to the fluid by a pump or determines the required volume flow (\( Q \)) based on water horsepower, differential head (\( h \)), specific gravity (\( SG \)), and pump efficiency (\( \mu \)).
Purpose: It is used in mechanical engineering to determine the theoretical power required to pump a fluid or the flow rate needed for a given power, aiding in pump selection, system design, and performance analysis.
The calculator uses the relationship:
or its inverse:
Where:
Explanation: Select whether to calculate water horsepower (\( P_{whp} \)) or volume flow (\( Q \)). For \( P_{whp} \), enter the volume flow, differential head, pump efficiency, and select the specific gravity (or input a custom value). For \( Q \), enter the water horsepower, differential head, pump efficiency, and specific gravity. The flow is converted to US gpm, and the head is converted to feet. The result is computed accordingly. Results are displayed with 5 decimal places, using scientific notation if the value exceeds 100,000 or is less than 0.0001. For default inputs (\( Q = 100 \, \text{gpm} \), \( h = 100 \, \text{ft} \), \( SG = 1.000 \) for water, \( \mu = 0.8 \)), the calculated water horsepower is approximately 3.12500 hp (2.32969 kW). For default inputs (\( P_{whp} = 3.125 \, \text{hp} \), \( h = 100 \, \text{ft} \), \( SG = 1.000 \), \( \mu = 0.8 \)), the calculated flow is approximately 100.00000 gpm.
Details: Calculating water horsepower or required flow is essential for determining the theoretical power required to move a fluid or sizing the flow for a given power, which helps in selecting the appropriate pump size, optimizing efficiency, and ensuring effective system performance.
How do I calculate water horsepower or volume flow?
Select whether to calculate water horsepower (\( P_{whp} \)) or volume flow (\( Q \)). For \( P_{whp} \), enter the volume flow, differential head, pump efficiency, and specific gravity (or custom value). For \( Q \), enter the water horsepower, differential head, pump efficiency, and specific gravity. Use the formula \( P_{whp} = \frac{Q h SG}{3960 \mu} \) or \( Q = \frac{P_{whp} \cdot 3960 \cdot \mu}{h SG} \).
What does water horsepower represent?
Water horsepower (\( P_{whp} \)) represents the theoretical power required to move a fluid against a given head, accounting for flow rate, specific gravity, and pump efficiency, while \( Q \) is the flow rate needed for a given power.
What is the formula for water horsepower or flow calculation?
The formula is \( P_{whp} = \frac{Q h SG}{3960 \mu} \) for water horsepower, or \( Q = \frac{P_{whp} \cdot 3960 \cdot \mu}{h SG} \) for flow, where \( Q \) is in US gpm, \( h \) is in feet, \( SG \) is the specific gravity, and \( \mu \) is the pump efficiency.
Can I use different units for flow, head, or select different specific gravities?
Yes, the calculator supports flow in US gpm, L/s, or m³/h, head in feet, meters, centimeters, inches, or yards, and allows selection of specific gravity for various liquids or a custom input. All inputs are converted to their base units for calculation.
What happens if I enter zero for head, efficiency, or specific gravity?
Entering zero for the head (\( h \)), pump efficiency (\( \mu \)), or specific gravity (\( SG \)) will result in the calculation not being performed, as the formula involves division by these values (for \( Q \)) or requires positive values (for \( P_{whp} \)). All must be greater than zero for a valid result.