How to calculate the discharge head of a vertical mixed flow pump?
As a supplier of Vertical Mixed Flow Pumps, I often receive inquiries from customers about how to calculate the discharge head of these pumps. Understanding the discharge head is crucial for proper pump selection and system design. In this blog post, I will explain the key concepts and steps involved in calculating the discharge head of a vertical mixed flow pump.
Understanding the Basics of Discharge Head
The discharge head of a pump refers to the total energy per unit weight of the fluid that the pump imparts to the fluid. It is a measure of the pump's ability to lift and move the fluid against gravity and overcome friction losses in the piping system. The discharge head is typically expressed in units of length, such as meters or feet.
There are two main components of the discharge head: the static head and the friction head.
Static Head
The static head is the vertical distance between the pump centerline and the highest point of the discharge point in the system. It represents the energy required to lift the fluid against gravity. There are two types of static head: the suction static head and the discharge static head.
- Suction Static Head: If the fluid source is above the pump centerline, the suction static head is positive. If the fluid source is below the pump centerline, the suction static head is negative, and it is often referred to as the suction lift.
- Discharge Static Head: This is the vertical distance from the pump centerline to the highest point of the discharge.
Friction Head
The friction head is the energy loss due to the friction between the fluid and the inner surface of the pipes, fittings, valves, and other components in the piping system. The friction head depends on several factors, including the flow rate, pipe diameter, pipe length, roughness of the pipe interior, and the type of fittings and valves used.
Steps to Calculate the Discharge Head
To calculate the discharge head of a vertical mixed flow pump, you can follow these steps:
Step 1: Determine the Static Head
- Measure or obtain the elevation difference between the fluid source and the pump centerline to determine the suction static head (Hss).
- Measure or obtain the elevation difference between the pump centerline and the highest point of the discharge to determine the discharge static head (Hds).
- The total static head (Hst) is the sum of the suction static head and the discharge static head: Hst = Hss + Hds
Step 2: Calculate the Friction Head
- Flow Rate: First, determine the required flow rate (Q) of the system. This is usually based on the application requirements, such as the amount of water needed for irrigation or the volume of fluid to be transferred in a given time.
- Pipe Characteristics: Gather information about the pipe system, including the pipe diameter (D), pipe length (L), and the roughness of the pipe interior (ε). Different types of pipes have different roughness values. For example, smooth plastic pipes have lower roughness compared to cast - iron pipes.
- Friction Factor: Use a method to calculate the friction factor (f). One common method is the Colebrook - White equation or the Moody chart. For laminar flow (Reynolds number Re < 2000), the friction factor can be calculated using the formula f = 64/Re, where Re = ρVD/μ (ρ is the fluid density, V is the fluid velocity, D is the pipe diameter, and μ is the fluid dynamic viscosity). For turbulent flow, the calculation is more complex, and the Moody chart or empirical correlations are often used.
- Friction Head Formula: The friction head (Hf) can be calculated using the Darcy - Weisbach equation: Hf = f * (L/D) * (V²/2g), where V is the fluid velocity in the pipe (V = Q/A, A is the cross - sectional area of the pipe), g is the acceleration due to gravity (g = 9.81 m/s²).
- Fittings and Valves: In addition to the pipe friction, you need to account for the friction losses in fittings and valves. Each fitting and valve has an equivalent length (Le) that can be added to the actual pipe length. The friction head due to fittings and valves can be calculated in the same way as the pipe friction head.
Step 3: Calculate the Discharge Head
The discharge head (Hd) of the pump is the sum of the total static head and the total friction head: Hd = Hst+ Hf
Example Calculation
Let's assume we have a vertical mixed flow pump system for an irrigation application.
- The water source is a well, and the water level in the well is 2 meters below the pump centerline (suction lift, Hss=- 2m).
- The discharge point is a sprinkler system located 10 meters above the pump centerline (discharge static head, Hds = 10m). So, the total static head Hst=Hss + Hds=-2 + 10 = 8m.
- The required flow rate Q is 50 m³/h. The pipe diameter D is 100 mm (0.1 m), and the pipe length L is 50 m. The pipe is made of PVC, with a roughness ε = 0.0015 mm.
- First, calculate the fluid velocity V: A = π * (D²/4)=π*(0.1²/4)=0.00785 m². V = Q/(3600 * A)=50/(3600 * 0.00785)≈1.77 m/s.
- Calculate the Reynolds number Re = ρVD/μ. Assuming water at 20°C, ρ = 1000 kg/m³ and μ = 0.001 Pa·s. Re=(1000 * 1.77 * 0.1)/0.001 = 177000 (turbulent flow).
- Using the Moody chart or an appropriate correlation, assume the friction factor f = 0.02.
- Calculate the friction head Hf = f * (L/D) * (V²/2g)=0.02*(50/0.1)*(1.77²/(2 * 9.81))≈1.58m.
- The discharge head Hd = Hst + Hf=8 + 1.58 = 9.58m
Importance of Accurate Discharge Head Calculation
Accurately calculating the discharge head is essential for several reasons:
- Pump Selection: It helps in selecting the right pump for the application. If the calculated discharge head is too low, the pump may not be able to lift the fluid to the required height or overcome the friction losses. If the calculated discharge head is too high, an oversized pump may be selected, which can lead to higher energy consumption and unnecessary costs.
- System Performance: A properly calculated discharge head ensures that the pump operates within its optimal range, providing efficient and reliable performance. It helps to avoid issues such as cavitation, which can damage the pump and reduce its lifespan.
Our Vertical Mixed Flow Pumps
At our company, we offer a wide range of Mixed Flow Centrifugal Pumps that are suitable for various applications. Our Sand Irrigation Sewage Mixed Flow Pumps are designed to handle fluids with sand and other solid particles, making them ideal for irrigation and sewage applications. We also have Vacuum Centrifugal Vertical Mixed Flow Pumps that can operate under vacuum conditions.
If you are in need of a vertical mixed flow pump for your project, and you are unsure about the discharge head calculation or which pump to choose, our team of experts is here to help. We can assist you in accurately calculating the discharge head and selecting the most suitable pump for your specific requirements. Contact us for more information and to start a procurement discussion.
References
- Crane, D. S. (1988). Flow of Fluids Through Valves, Fittings, and Pipe. Technical Paper No. 410M. Crane Co.
- Streeter, V. L., & Wylie, E. B. (1981). Fluid Mechanics. McGraw - Hill.