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Definition: This calculator computes the maximum shut-off head (\( h_s \)) of a centrifugal pump, based on the outside diameter of the impeller (\( d \)) and the wheel velocity (\( n \)).
Purpose: It is used in mechanical engineering to estimate the maximum pressure head a centrifugal pump can generate when its discharge is completely closed, which is critical for pump design and system safety.
The calculator uses the relationship:
Where:
Explanation: Enter the outside diameter of the impeller and the wheel velocity in the chosen units. The diameter is converted to inches, and the velocity is converted to rpm. The shut-off head is calculated as \( h_s = \left( \frac{d \cdot n}{1840} \right)^2 \). 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 (\( d = 10 \, \text{in} \), \( n = 1800 \, \text{rpm} \)), the calculated shut-off head \( h_s \) is approximately 95.58824 ft.
Details: Calculating the shut-off head for a centrifugal pump is essential for understanding the maximum pressure the pump can generate, which is critical for system design, ensuring safe operation, and preventing damage to the pump or piping system.
How do I calculate the shut-off head for a centrifugal pump?
Measure the outside diameter of the impeller (\( d \)) in inches and the wheel velocity (\( n \)) in rpm. Compute the shut-off head using the formula \( h_s = \left( \frac{d \cdot n}{1840} \right)^2 \). The result will be in feet.
What does the shut-off head represent?
The shut-off head (\( h_s \)) represents the maximum pressure head a centrifugal pump can generate when its discharge is completely closed, indicating the pump's maximum capability under no-flow conditions.
What is the formula for the shut-off head?
The formula for the shut-off head is \( h_s = \left( \frac{d \cdot n}{1840} \right)^2 \), where \( d \) is the impeller diameter in inches, and \( n \) is the wheel velocity in rpm. The standard unit for the result in this calculator is feet (ft).
Can I use different units for the impeller diameter and wheel velocity?
Yes, the calculator supports multiple units for the impeller diameter (in, cm, m) and wheel velocity (rpm, rad/s, Hz). All inputs are converted to inches and rpm, respectively, for the calculation.
What happens if I enter a negative value for the diameter or velocity?
Entering a negative value for the impeller diameter (\( d \)) or wheel velocity (\( n \)) will result in the calculation not being performed, as these values must be non-negative for a valid result.