Angular Speed of Vane Pump given Theoretical Discharge Calculator

✖Theoretical Discharge of Pump in Vane Pump is the volume of liquid pumped out in unit time.ⓘ Theoretical Discharge of Pump in Vane Pump [Q_vp]			+10% -10%
✖Eccentricity of a pump is the difference between cam ring diameter and rotor diameter.ⓘ Eccentricity [e]			+10% -10%
✖Width of Rotor in vane Pump is the width of the rotor of a pump.ⓘ Width of Rotor in Vane Pump [w_vp]			+10% -10%
✖Diameter of cam ring is the diameter of cam ring of a vane pump.ⓘ Diameter of Cam Ring [d_c]			+10% -10%
✖Diameter of rotor is the value of diameter of the rotor of a pump.ⓘ Diameter of Rotor [d_r]			+10% -10%

✖The Angular Speed of Driving Member in RPM is the rate of change of angular position of the driving or the input member.ⓘ Angular Speed of Vane Pump given Theoretical Discharge [N₁]

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Angular Speed of Vane Pump given Theoretical Discharge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Speed of Driving Member = (2*Theoretical Discharge of Pump in Vane Pump)/(pi*Eccentricity*Width of Rotor in Vane Pump*(Diameter of Cam Ring+Diameter of Rotor))
N₁ = (2*Q_vp)/(pi*e*w_vp*(d_c+d_r))
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Angular Speed of Driving Member - (Measured in Radian per Second) - The Angular Speed of Driving Member in RPM is the rate of change of angular position of the driving or the input member.
Theoretical Discharge of Pump in Vane Pump - (Measured in Cubic Meter per Second) - Theoretical Discharge of Pump in Vane Pump is the volume of liquid pumped out in unit time.
Eccentricity - (Measured in Meter) - Eccentricity of a pump is the difference between cam ring diameter and rotor diameter.
Width of Rotor in Vane Pump - (Measured in Meter) - Width of Rotor in vane Pump is the width of the rotor of a pump.
Diameter of Cam Ring - (Measured in Meter) - Diameter of cam ring is the diameter of cam ring of a vane pump.
Diameter of Rotor - (Measured in Meter) - Diameter of rotor is the value of diameter of the rotor of a pump.

STEP 1: Convert Input(s) to Base Unit

Theoretical Discharge of Pump in Vane Pump: 0.84 Cubic Meter per Second --> 0.84 Cubic Meter per Second No Conversion Required
Eccentricity: 0.01 Meter --> 0.01 Meter No Conversion Required
Width of Rotor in Vane Pump: 20.37 Meter --> 20.37 Meter No Conversion Required
Diameter of Cam Ring: 0.075 Meter --> 0.075 Meter No Conversion Required
Diameter of Rotor: 0.05 Meter --> 0.05 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N₁ = (2*Q_vp)/(pi*e*w_vp*(d_c+d_r)) --> (2*0.84)/(pi*0.01*20.37*(0.075+0.05))

Evaluating ... ...

N₁ = 21.0018893976934

STEP 3: Convert Result to Output's Unit

21.0018893976934 Radian per Second -->200.553270724943 Revolution per Minute (Check conversion here)

FINAL ANSWER

200.553270724943 ≈ 200.5533 Revolution per Minute <-- Angular Speed of Driving Member

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Fluid Machinery » Hydraulic Pumps » Mechanical » Vane Pumps » Angular Speed of Vane Pump given Theoretical Discharge

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Created by Sagar S Kulkarni

Dayananda Sagar College of Engineering (DSCE), Bengaluru

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National Institute of Technology (NIT), Tiruchirapalli

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< Vane Pumps Calculators

Volumetric Displacement of Vane Pumps

LaTeX Go Theoretical Volumetric Displacement = pi/2*Eccentricity*Width of Rotor in Vane Pump*(Diameter of Cam Ring+Diameter of Rotor)

Vane Pump Constant

LaTeX Go Vane Pump Constant = pi/2*Width of Rotor in Vane Pump*(Diameter of Cam Ring+Diameter of Rotor)

Theoretical Discharge of Vane Pump

LaTeX Go Theoretical Discharge of Pump in Vane Pump = Theoretical Volumetric Displacement*Angular Speed of Driving Member

Eccentricity of Vane Pump

LaTeX Go Eccentricity = (Diameter of Cam Ring-Diameter of Rotor)/2

Angular Speed of Vane Pump given Theoretical Discharge Formula

LaTeX Go

What is theoretical discharge?

Theoretical discharge, also called as flow capacity of a pump is the volume of liquid discharged per unit time.

How to Calculate Angular Speed of Vane Pump given Theoretical Discharge?

Angular Speed of Vane Pump given Theoretical Discharge calculator uses Angular Speed of Driving Member = (2*Theoretical Discharge of Pump in Vane Pump)/(pi*Eccentricity*Width of Rotor in Vane Pump*(Diameter of Cam Ring+Diameter of Rotor)) to calculate the Angular Speed of Driving Member, Angular Speed of Vane Pump given Theoretical Discharge formula is defined as the rotational speed of the vane pump that is theoretically calculated based on the pump's design parameters and operating conditions, providing an idealized value for the pump's performance. Angular Speed of Driving Member is denoted by N₁ symbol.

How to calculate Angular Speed of Vane Pump given Theoretical Discharge using this online calculator? To use this online calculator for Angular Speed of Vane Pump given Theoretical Discharge, enter Theoretical Discharge of Pump in Vane Pump (Q_vp), Eccentricity (e), Width of Rotor in Vane Pump (w_vp), Diameter of Cam Ring (d_c) & Diameter of Rotor (d_r) and hit the calculate button. Here is how the Angular Speed of Vane Pump given Theoretical Discharge calculation can be explained with given input values -> 1915.143 = (2*0.84)/(pi*0.01*20.37*(0.075+0.05)).

FAQ

What is Angular Speed of Vane Pump given Theoretical Discharge?

Angular Speed of Vane Pump given Theoretical Discharge formula is defined as the rotational speed of the vane pump that is theoretically calculated based on the pump's design parameters and operating conditions, providing an idealized value for the pump's performance and is represented as N₁ = (2*Q_vp)/(pi*e*w_vp*(d_c+d_r)) or Angular Speed of Driving Member = (2*Theoretical Discharge of Pump in Vane Pump)/(pi*Eccentricity*Width of Rotor in Vane Pump*(Diameter of Cam Ring+Diameter of Rotor)). Theoretical Discharge of Pump in Vane Pump is the volume of liquid pumped out in unit time, Eccentricity of a pump is the difference between cam ring diameter and rotor diameter, Width of Rotor in vane Pump is the width of the rotor of a pump, Diameter of cam ring is the diameter of cam ring of a vane pump & Diameter of rotor is the value of diameter of the rotor of a pump.

How to calculate Angular Speed of Vane Pump given Theoretical Discharge?

Angular Speed of Vane Pump given Theoretical Discharge formula is defined as the rotational speed of the vane pump that is theoretically calculated based on the pump's design parameters and operating conditions, providing an idealized value for the pump's performance is calculated using Angular Speed of Driving Member = (2*Theoretical Discharge of Pump in Vane Pump)/(pi*Eccentricity*Width of Rotor in Vane Pump*(Diameter of Cam Ring+Diameter of Rotor)). To calculate Angular Speed of Vane Pump given Theoretical Discharge, you need Theoretical Discharge of Pump in Vane Pump (Q_vp), Eccentricity (e), Width of Rotor in Vane Pump (w_vp), Diameter of Cam Ring (d_c) & Diameter of Rotor (d_r). With our tool, you need to enter the respective value for Theoretical Discharge of Pump in Vane Pump, Eccentricity, Width of Rotor in Vane Pump, Diameter of Cam Ring & Diameter of Rotor and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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