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Centrifugal pumps are widely used in various industries for moving liquids and gases. The impeller is a crucial component of a centrifugal pump that imparts energy to the liquid by rotating at high speeds. Understanding the velocity triangles associated with the impeller is essential for optimizing pump performance and efficiency.
Inlet and outlet velocity triangles for Centrifugal Pump Work done By Impeller on liquid 1. 0Liquid enters eye of impeller in radial direction i.e. α = 90, 𝑉 ê1 =0, V
Inlet and Outlet Velocity Triangles for Centrifugal Pump Impeller
When liquid enters the eye of the impeller in a radial direction (α = 90°), the inlet velocity component (V₁) is zero. The liquid is then accelerated by the impeller blades, resulting in an outlet velocity (V₂) in the tangential direction. The impeller imparts kinetic energy to the liquid, which is converted into pressure energy as the liquid flows through the pump.
The velocity triangles for the inlet and outlet of the impeller can be represented as follows:
- Inlet Velocity Triangle:
- Inlet Blade Angle (α₁) = 90°
- Inlet Velocity (V₁) = 0
- Absolute Velocity (V₁) = V₁
- Relative Velocity (W₁) = V₁
- Outlet Velocity Triangle:
- Outlet Blade Angle (β₂)
- Outlet Velocity (V₂)
- Absolute Velocity (V₂)
- Relative Velocity (W₂)
Work Done by Impeller on Liquid
The impeller of a centrifugal pump performs work on the liquid by increasing its kinetic energy. The work done by the impeller can be calculated using the following formula:
\[ W = m * (V₂² - V₁²) / 2 \]
Where:
- W = Work done by the impeller on the liquid
- m = Mass flow rate of the liquid
- V₁ = Inlet velocity of the liquid
- V₂ = Outlet velocity of the liquid
The impeller imparts energy to the liquid, which results in an increase in velocity and pressure. This work done by the impeller is crucial for maintaining the flow of liquid through the pump and overcoming the system resistance.
Centrifugal Pump Velocity Diagram
The velocity diagram for a centrifugal pump illustrates the velocity components at the inlet and outlet of the impeller. By analyzing the velocity triangles, engineers can optimize the design of the impeller to achieve the desired flow rate and pressure head.
The velocity diagram includes the following components:
- Inlet Velocity (V₁)
- Outlet Velocity (V₂)
- Absolute Velocity (V)
- Relative Velocity (W)
- Blade Angles (α, β)
By understanding the velocity diagram, engineers can make informed decisions regarding the impeller design, blade angles, and pump operation parameters to maximize efficiency and performance.
How to Calculate Pump Velocity
The pump velocity can be calculated using the following formula:
\[ V = Q / A \]
Where:
- V = Pump velocity
- Q = Flow rate of the liquid
- A = Area of the pump inlet or outlet
Calculating the pump velocity is essential for determining the speed at which the liquid is being pumped through the system. By monitoring the pump velocity, engineers can ensure that the pump is operating within its design parameters and delivering the required flow rate.
Triangular Velocity Diagram
The triangular velocity diagram is a graphical representation of the velocity components at the inlet and outlet of the impeller. By plotting the velocity triangles on a triangular diagram, engineers can visualize the flow patterns and energy transfer within the pump.
The triangular velocity diagram includes the following elements:
- Inlet Velocity Triangle
- Outlet Velocity Triangle
- Absolute Velocity Components
- Relative Velocity Components
- Blade Angles
Analyzing the triangular velocity diagram allows engineers to optimize the impeller design, blade angles, and pump operation parameters for maximum efficiency and performance.
Centrifugal Pump Discharge Formula
The discharge of a centrifugal pump can be calculated using the following formula:
\[ Q = A * V \]
Where:
- Q = Flow rate of the liquid
- A = Area of the pump inlet or outlet
- V = Pump velocity
The discharge formula is essential for determining the volumetric flow rate of the liquid through the pump. By calculating the discharge, engineers can ensure that the pump is delivering the required flow rate to meet the process demands.
Manometric Head in Centrifugal Pump
The manometric head in a centrifugal pump is a measure of the pressure energy imparted to the liquid by the impeller. It represents the height to which the pump can raise the liquid against gravity. The manometric head can be calculated using the following formula:
\[ H_m = (P₂ - P₁) / (ρ * g) + (V₂² - V₁²) / (2 * g) \]
Where:
- Hm = Manometric head
- P₁, P₂ = Pressure at the inlet and outlet of the pump
- ρ = Density of the liquid
- g = Acceleration due to gravity
- V₁, V₂ = Inlet and outlet velocities of the liquid
Subject - Fluid Mechanics and MachineryChapter - Inlet and Outlet Velocity Triangles Diagram For Impeller of Centrifugal PumpTimestamps0:00 - Start0:07 - Vel...
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centrifugal pump impeller velocity triangles|velocity triangle diagram