When it comes to industrial applications, high pressure centrifugal pumps play a crucial role in various processes. As a leading supplier of high pressure centrifugal pumps, I often receive inquiries from clients about how to calculate the total head and flow rate when these pumps are connected in series. In this blog post, I will delve into the details of this topic, providing a comprehensive guide on the calculations and considerations involved.
Understanding High Pressure Centrifugal Pumps
Before we dive into the calculations, let's briefly understand what high pressure centrifugal pumps are. These pumps are designed to generate high pressure by using centrifugal force to transfer fluids. They are commonly used in applications such as water supply, oil and gas, chemical processing, and power generation.
High pressure centrifugal pumps come in different types, including Horizontal Centrifugal Pump, Corrosion Resistant Centrifugal Pump, and Vertical Centrifugal Pump. Each type has its own advantages and is suitable for specific applications.
Connecting High Pressure Centrifugal Pumps in Series
Connecting high pressure centrifugal pumps in series means that the outlet of one pump is connected to the inlet of the next pump. This configuration is used to increase the total head (pressure) of the system while maintaining a relatively constant flow rate. When pumps are connected in series, the heads of the individual pumps are added together, while the flow rate remains the same.
Calculating the Total Head
The total head of a series pump system is the sum of the heads of the individual pumps. To calculate the total head, you need to know the head - flow characteristics of each pump. These characteristics are usually provided by the pump manufacturer in the form of a pump curve.
Let's assume we have two high pressure centrifugal pumps, Pump A and Pump B, connected in series. The head of Pump A at a given flow rate (Q) is (H_A), and the head of Pump B at the same flow rate (Q) is (H_B). The total head (H_{total}) of the series system is given by the formula:
[H_{total}=H_A + H_B]
In practice, you need to select a common flow rate for both pumps. This is because the flow rate through each pump in a series system is the same. You can use the pump curves to find the heads of each pump at the selected flow rate and then add them together to get the total head.
For example, if at a flow rate of (Q = 100\ m^3/h), Pump A has a head of (H_A= 50\ m) and Pump B has a head of (H_B = 60\ m), then the total head of the series system at this flow rate is (H_{total}=50 + 60=110\ m)
Calculating the Flow Rate
When high pressure centrifugal pumps are connected in series, the flow rate through the system is determined by the system curve and the combined pump curve of the series pumps. The system curve represents the relationship between the head required by the system and the flow rate. The combined pump curve of the series pumps is obtained by adding the heads of the individual pumps at each flow rate.
The intersection of the system curve and the combined pump curve gives the operating point of the series pump system, which determines the flow rate and the total head of the system.
To find the flow rate, you can follow these steps:
- Obtain the system curve equation or plot. The system curve is usually a quadratic function of the form (H_{system}=H_0+KQ^2), where (H_0) is the static head and (K) is a coefficient related to the friction losses in the system.
- Obtain the pump curves of the individual pumps.
- Create the combined pump curve by adding the heads of the individual pumps at each flow rate.
- Plot the system curve and the combined pump curve on the same graph.
- Find the intersection point of the two curves. The (x) - coordinate of this point is the flow rate of the series pump system.
Considerations when Connecting Pumps in Series
- Pump Selection: It is important to select pumps that are compatible with each other in terms of flow rate and head characteristics. Pumps with similar flow - head curves are generally easier to operate in series.
- Cavitation: Cavitation can occur if the suction pressure of a pump is too low. When pumps are connected in series, the suction pressure of the second pump is affected by the discharge pressure of the first pump. Make sure that the suction pressure of each pump is above the critical value to avoid cavitation.
- Motor Power: The motor power required for a series pump system is higher than that for a single - pump system. You need to ensure that the motors of the individual pumps are sized correctly to handle the increased load.
Practical Example
Let's consider a practical example of a water supply system where two high pressure centrifugal pumps are connected in series. The system has a static head of (H_0 = 20\ m) and a friction coefficient (K = 0.01\ m/(m^3/h)^2). The system curve equation is (H_{system}=20 + 0.01Q^2)
Pump A has the following head - flow relationship: (H_A=80-0.02Q^2)
Pump B has the following head - flow relationship: (H_B=70 - 0.015Q^2)
The combined pump curve is (H_{combined}=H_A + H_B=(80-0.02Q^2)+(70 - 0.015Q^2)=150-0.035Q^2)
To find the operating point, we set the system curve equal to the combined pump curve:
[20 + 0.01Q^2=150-0.035Q^2]
[0.01Q^2+0.035Q^2=150 - 20]
[0.045Q^2=130]
[Q^2=\frac{130}{0.045}\approx2888.89]
[Q\approx53.75\ m^3/h]
Substitute (Q) into the system curve to find the total head:
[H_{total}=20+0.01\times(53.75)^2=20 + 0.01\times2889.06=20 + 28.89 = 48.89\ m]
Conclusion
Connecting high pressure centrifugal pumps in series is an effective way to increase the total head of a system while maintaining a relatively constant flow rate. By understanding how to calculate the total head and flow rate of a series pump system, you can design and operate your pumping systems more efficiently.
As a supplier of high pressure centrifugal pumps, we offer a wide range of pumps with different specifications to meet your specific needs. If you are interested in purchasing high pressure centrifugal pumps or need more information on pump selection and system design, please feel free to contact us for procurement and further discussions.
References
- Pump Handbook, Karassik et al.
- Fluid Mechanics and Machinery, R. K. Bansal.
