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*Qvp)/(pi*e*wvp*(dc+dr))
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*Qvp)/(pi*e*wvp*(dc+dr)) --> (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)

Credits

Created by Sagar S Kulkarni
Dayananda Sagar College of Engineering (DSCE), Bengaluru
Sagar S Kulkarni has created this Calculator and 200+ more calculators!
Verified by Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
Vaibhav Malani has verified this Calculator and 200+ more calculators!

8 Vane Pumps Calculators

Angular Speed of Vane Pump given Theoretical Discharge
Go 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))
Width of Vane Pump given Theoretical Discharge
Go Width of Rotor in Vane Pump = (2*Theoretical Discharge of Pump in Vane Pump)/(pi*Eccentricity*Angular Speed of Driving Member*(Diameter of Cam Ring+Diameter of Rotor))
Theoretical Discharge of Vane Pump given diameter of Camring and Rotor
Go Theoretical Discharge of Pump in Vane Pump = pi/2*Eccentricity*Width of Rotor in Vane Pump*(Diameter of Cam Ring+Diameter of Rotor)*Angular Speed of Driving Member
Width of Rotor of Vane Pump given Volumetric Displacement
Go Width of Rotor in Vane Pump = (2*Theoretical Volumetric Displacement)/(pi*Eccentricity*(Diameter of Cam Ring+Diameter of Rotor))
Volumetric Displacement of Vane Pumps
Go Theoretical Volumetric Displacement = pi/2*Eccentricity*Width of Rotor in Vane Pump*(Diameter of Cam Ring+Diameter of Rotor)
Vane Pump Constant
Go Vane Pump Constant = pi/2*Width of Rotor in Vane Pump*(Diameter of Cam Ring+Diameter of Rotor)
Theoretical Discharge of Vane Pump
Go Theoretical Discharge of Pump in Vane Pump = Theoretical Volumetric Displacement*Angular Speed of Driving Member
Eccentricity of Vane Pump
Go Eccentricity = (Diameter of Cam Ring-Diameter of Rotor)/2

Angular Speed of Vane Pump given Theoretical Discharge Formula

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*Qvp)/(pi*e*wvp*(dc+dr))

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 is a measure of how quickly the vane or rotor of the pump rotates. It is typically expressed in terms of revolutions per minute (RPM) or radians per second (rad/s). 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 (Qvp), Eccentricity (e), Width of Rotor in Vane Pump (wvp), Diameter of Cam Ring (dc) & Diameter of Rotor (dr) 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 is a measure of how quickly the vane or rotor of the pump rotates. It is typically expressed in terms of revolutions per minute (RPM) or radians per second (rad/s) and is represented as N1 = (2*Qvp)/(pi*e*wvp*(dc+dr)) 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 is a measure of how quickly the vane or rotor of the pump rotates. It is typically expressed in terms of revolutions per minute (RPM) or radians per second (rad/s) 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 (Qvp), Eccentricity (e), Width of Rotor in Vane Pump (wvp), Diameter of Cam Ring (dc) & Diameter of Rotor (dr). 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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