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Centrifugal pumps are widely used in various industries for moving fluids from one place to another. One of the key parameters to consider when selecting a centrifugal pump is the pump head, which is a measure of the energy imparted to the fluid by the pump. In this article, we will discuss the centrifugal pump head calculation formula and provide an example to illustrate how to calculate the head of a centrifugal pump.
1. Calculate the total head and select the pump. 2. Calculate the NPSH available and check with respect to the NPSH required. 3. Calculate the specific speed and predict the pump efficiency. Calculate the suction specific speed and Thoma number and check the prediction of the
Centrifugal Pump Head Calculation Formula
The total head (H) of a centrifugal pump can be calculated using the following formula:
\[ H = \frac{P_{outlet} - P_{inlet}}{\rho \cdot g} + \frac{v_{outlet}^2 - v_{inlet}^2}{2 \cdot g} + z_{outlet} - z_{inlet} \]
Where:
- \( P_{outlet} \) = Pressure at the outlet (Pa)
- \( P_{inlet} \) = Pressure at the inlet (Pa)
- \( \rho \) = Density of the fluid (kg/m³)
- \( g \) = Acceleration due to gravity (m/s²)
- \( v_{outlet} \) = Velocity at the outlet (m/s)
- \( v_{inlet} \) = Velocity at the inlet (m/s)
- \( z_{outlet} \) = Elevation at the outlet (m)
- \( z_{inlet} \) = Elevation at the inlet (m)
Pump Head Calculation Example
Let's consider an example to calculate the head of a centrifugal pump. Assume we have a centrifugal pump pumping water at 20°C with a flow rate of 10 L/s. The vacuum gauge at the inlet reads 0.031 MPa, and the pressure gauge at the outlet reads 0.126 MPa (gauge pressure). The density of water at 20°C is approximately 998 kg/m³.
Given:
- Flow rate (Q) = 10 L/s = 0.01 m³/s
- Inlet pressure (P_{inlet}) = 0.031 MPa = 31,000 Pa
- Outlet pressure (P_{outlet}) = 0.126 MPa = 126,000 Pa
- Density of water (\( \rho \)) = 998 kg/m³
- Acceleration due to gravity (\( g \)) = 9.81 m/s²
- Inlet velocity (v_{inlet}) = 0 m/s (assumed)
- Outlet velocity (v_{outlet}) = Q / A_{outlet}, where A_{outlet} is the outlet area
Next, we need to calculate the elevation difference (\( z_{outlet} - z_{inlet} \)). If the pump is installed horizontally, this term can be neglected.
Now, we can substitute the given values into the total head formula to calculate the head of the centrifugal pump.
\[ H = \frac{126,000 - 31,000}{998 \cdot 9.81} + \frac{v_{outlet}^2 - 0}{2 \cdot 9.81} \]
\[ H = \frac{95,000}{9,807} + \frac{v_{outlet}^2}{19.62} \]
\[ H = 9.68 + \frac{v_{outlet}^2}{19.62} \]
What is head and how is it used in a pump system to make calculations easier? …
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centrifugal pump head calculation example|pump head height calculator