Head Pump Equation

[Roshan Fried]

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Pump head calculations are fundamental in the world of fluid mechanics and engineering. They play a crucial role in determining the performance and efficiency of pumps in various applications, ranging from industrial processes to municipal water supply systems. In this article, we will delve into the essential concepts and equations involved in pump head calculations, shedding light on the significance of these calculations in engineering design.

Pump head, often referred to as total head or total dynamic head (TDH), represents the total energy imparted to a fluid by a pump. It quantifies the combination of pressure energy and kinetic energy that a pump imparts to the fluid as it moves through the system. Understanding pump head is essential because it helps engineers assess the pump's performance, select the right pump for a given application, and design efficient fluid transport systems.

• Static Head (Hs): Static head is the vertical distance between the pump's suction and discharge points. It accounts for the potential energy change due to elevation. If the discharge point is higher than the suction point, static head is positive, and if it's lower, static head is negative.
• Velocity Head (Hv): Velocity head is the kinetic energy imparted to the fluid as it moves through the pipes. It depends on the fluid's velocity and is calculated using the equation:

• Pressure Head (Hp): Pressure head represents the energy added to the fluid by the pump to overcome pressure losses in the system. It can be calculated using Bernoulli's equation:

Understanding this equation allows engineers to design efficient pump systems by considering factors such as the required flow rate, pipe dimensions, elevation differences, and pressure requirements.

1. Pump Selection: Engineers use pump head calculations to select the appropriate pump for a specific application. By determining the required total head, they can choose a pump that can meet these requirements efficiently.
2. System Design: Pump head calculations are crucial in designing fluid transport systems. Engineers can size pipes and select appropriate fittings to minimize friction losses and maximize system efficiency.
3. Energy Efficiency: Understanding pump head helps in optimizing pump operation for energy efficiency. By minimizing unnecessary head, engineers can reduce energy consumption and operating costs.
4. Maintenance and Troubleshooting: Monitoring pump head over time can help detect changes in system performance, indicating the need for maintenance or troubleshooting issues such as blockages or leaks.

To illustrate the concept of pump head calculations, let's consider a simplified scenario involving a water pump used for irrigation. In this scenario, we want to determine the total pump head required for efficient water distribution from a reservoir to a field.

In this example, the total pump head required for the irrigation system is 30 meters. This means the pump must be able to provide enough energy to lift the water 20 meters vertically, overcome frictional losses, maintain a certain velocity, and provide additional pressure as needed.

The Euler pump and turbine equations are the most fundamental equations in the field of turbomachinery. These equations govern the power, efficiencies and other factors that contribute to the design of turbomachines. With the help of these equations the head developed by a pump and the head utilised by a turbine can be easily determined. As the name suggests these equations were formulated by Leonhard Euler in the eighteenth century.[1] These equations can be derived from the moment of momentum equation when applied for a pump or a turbine.

Pumps are the devices used for transporting or pressurizing liquids and are indispensable in the wastewater treatment industry. Therefore, calculating the pump head is crucial. An insufficient head means the water cannot be pumped up, while an excessive head wastes energy. This article will guide you through the methods to calculate the pump head.

Calculate the head of a centrifugal pump pumping water at 20C with a flow rate of 10L/s. The vacuum gauge at the inlet reads 0.031Mpa, and the pressure gauge at the outlet reads 0.126Mpa (gauge pressure). The vertical distance between the two gauges is 80mm, with inlet diameter d1=80mm and outlet diameter d2=60mm

Using the diagram as an example, with known dimensions: A height of 5m, B length of 10m, C height of 11m, D length of 10m, and three elbows. The actual operational head would be calculated as follows:

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It is important to understand the nuances of what makes up the total head of the system as a function of flow rate and varying system conditions so that if a user is designing or operating a pump system, the pump can be selected and operated properly. Additionally, if the goal is to measure the pump performance after installation, it is important to understand how to do that in the same way that the pump manufacturer will.

Elevation head, which is the difference in elevation that liquid will travel. For example, if a user was pumping from one tank to another and the level in the tanks were the same, there would be zero elevation head. But if pumping from a tank at ground level to the roof of a 100-foot building, there would be 100 feet of elevation head.

Pressure head is the difference in pressure between source and destination. For example, if taking liquid from a lake at atmospheric pressure and delivering it to a tank that had 10 pounds per square inch (psi) above atmospheric pressure, the pressure head would be 10 psi expressed as feet of the liquid being pumped. The conversion between pressure and head is described in the pump total head measurement section.

Friction head is the head loss in the system due to friction and is a function of the liquids velocity or flow rate squared. As mentioned, the friction loss will depend on the flow rate but also the size of the piping, fittings, valves and end use equipment in the system. If there are control valves in the system that are used to actively regulate the flow rate, the friction loss across the control valve is referred to as control head. It is important to understand control head because it is often a source of energy consumption that can be improved.

Image 1 shows a pump system where liquid is delivered from a supply tank to three closed product tanks. Considering the equation for total head (system), the supply tank would be point 1 and the product tanks would be point 2. The elevation head would be the difference in elevation between the level in the product tank and the supply tank. The pressure head would be the pressure difference between the product tank and the supply tank expressed as feet of the liquid pumped. Friction head would include all of the losses from the supply tank, piping, fittings, heat exchanger, control valves, etc.

To measure the total head of the pump, pressure will be measured at points 1 and 2, the elevation from the pressure gauge to datum will be measured, and the velocity at the pressure measurement location will be calculated based on the volumetric flow rate and the pipe inside diameter. The pressure measured will need to be converted to feet of liquid based on Equation 3.

When doing the calculation, attention will need to be paid to units to get the calculation to come out correctly. With U.S. customary units, it is common to use a relative density called specific gravity and a conversion constant to convert pressure to feet. This can be done using Equation 4.

Total head is a fundamental that is beneficial to understand when working with pumping systems. It provides an understanding of the system requirements, valuable information for pump selection, and a key consideration of energy consumption. This article covers the basics but does not discuss in-depth review, calculation examples or scenarios that pump professionals will come across. For more information on this topic, including standards and training, visit www.pumps.org.

To select a right-sized centrifugal pump, a design or pump sales engineer needs to know the desired flow rate and total head. While flow rate is relatively intuitive (or customer-driven), determining pump total head can be more challenging and lead to serious issues if calculated incorrectly.

For example, if too many safety factors are integrated into the calculation, the result can be an oversized and more expensive pump. Alternatively, if not enough are considered, the risk is an undersized pump that cannot handle the work. One result of miscalculating the pump total head is incorrect sizing of the motor and related electrical components. Other consequences can include:

When calculating TDH, the energy available at the entrance of the pump is being compared to the energy needed at the discharge to produce the desired flow, and the pump is then selected to add the additional energy required at the discharge most efficiently. This is the head routinely specified for pumping applications.

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