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Angular Speed of Vane Pump given Theoretical Discharge Formula

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The Angular Speed of Driving Member in RPM is the rate of change of angular position of the driving or the input member. Check FAQs

N 1 = \frac{2 \cdot Q vp}{π \cdot e \cdot w vp \cdot (d c + d r)}

N₁ - Angular Speed of Driving Member?Q_vp - Theoretical Discharge of Pump in Vane Pump?e - Eccentricity?w_vp - Width of Rotor in Vane Pump?d_c - Diameter of Cam Ring?d_r - Diameter of Rotor?π - Archimedes' constant?

Angular Speed of Vane Pump given Theoretical Discharge Example

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Here is how the Angular Speed of Vane Pump given Theoretical Discharge equation looks like with Values.

Here is how the Angular Speed of Vane Pump given Theoretical Discharge equation looks like with Units.

Here is how the Angular Speed of Vane Pump given Theoretical Discharge equation looks like.

200.5533 = \frac{2 \cdot 0.84}{3.1416 \cdot 0.01 \cdot 20.37 \cdot (0.075 + 0.05)}

200.5533rev/min = \frac{2 \cdot 0.84m³/s}{3.1416 \cdot 0.01m \cdot 20.37m \cdot (0.075m + 0.05m)}

200.5533 = \frac{2 \cdot 0.84}{3.1416 \cdot 0.01 \cdot 20.37 \cdot (0.075 + 0.05)}

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Angular Speed of Vane Pump given Theoretical Discharge Solution

Follow our step by step solution on how to calculate Angular Speed of Vane Pump given Theoretical Discharge?

FIRST Step Consider the formula

N 1 = \frac{2 \cdot Q vp}{π \cdot e \cdot w vp \cdot (d c + d r)}

Next Step Substitute values of Variables

∴

N 1 = \frac{2 \cdot 0.84m³/s}{π \cdot 0.01m \cdot 20.37m \cdot (0.075m + 0.05m)}

Next Step Substitute values of Constants

∴

N 1 = \frac{2 \cdot 0.84m³/s}{3.1416 \cdot 0.01m \cdot 20.37m \cdot (0.075m + 0.05m)}

Next Step Prepare to Evaluate

∴

N 1 = \frac{2 \cdot 0.84}{3.1416 \cdot 0.01 \cdot 20.37 \cdot (0.075 + 0.05)}

Next Step Evaluate

∴

N 1 = 21.0018893976934rad/s

Next Step Convert to Output's Unit

∴

N 1 = 200.553270724943rev/min

LAST Step Rounding Answer

∴

N 1 = 200.5533rev/min

Angular Speed of Vane Pump given Theoretical Discharge Formula Elements

Variables

Constants

Angular Speed of Driving Member

The Angular Speed of Driving Member in RPM is the rate of change of angular position of the driving or the input member.

Symbol: N₁

Measurement: Angular VelocityUnit: rev/min

Note: Value should be greater than 0.

Formulas to find Angular Speed of Driving Member

Theoretical Discharge of Pump in Vane Pump

Theoretical Discharge of Pump in Vane Pump is the volume of liquid pumped out in unit time.

Symbol: Q_vp

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Theoretical Discharge of Pump in Vane Pump

Eccentricity

Eccentricity of a pump is the difference between cam ring diameter and rotor diameter.

Symbol: e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Eccentricity

Width of Rotor in Vane Pump

Width of Rotor in vane Pump is the width of the rotor of a pump.

Symbol: w_vp

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Width of Rotor in Vane Pump

Diameter of Cam Ring

Diameter of cam ring is the diameter of cam ring of a vane pump.

Symbol: d_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter of Cam Ring

Diameter of Rotor

Diameter of rotor is the value of diameter of the rotor of a pump.

Symbol: d_r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diameter of Rotor

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Vane Pumps category

Go Volumetric Displacement of Vane Pumps

V D = \frac{π}{2} \cdot e \cdot w vp \cdot (d c + d r)

Go Eccentricity of Vane Pump

e = \frac{d c - d r}{2}

Go Theoretical Discharge of Vane Pump

Q vp = V D \cdot N 1

Go Vane Pump Constant

K v = \frac{π}{2} \cdot w vp \cdot (d c + d r)

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

Angular Speed of Vane Pump given Theoretical Discharge evaluator 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 evaluate 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 evaluate Angular Speed of Vane Pump given Theoretical Discharge using this online evaluator? To use this online evaluator 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.

FAQs on Angular Speed of Vane Pump given Theoretical Discharge

What is the formula to find Angular Speed of Vane Pump given Theoretical Discharge?

The formula of Angular Speed of Vane Pump given Theoretical Discharge is expressed as 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)). Here is an example- 1915.143 = (2*0.84)/(pi*0.01*20.37*(0.075+0.05)).

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

With 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) we can find Angular Speed of Vane Pump given Theoretical Discharge using the 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)). This formula also uses Archimedes' constant .

Can the Angular Speed of Vane Pump given Theoretical Discharge be negative?

No, the Angular Speed of Vane Pump given Theoretical Discharge, measured in Angular Velocity cannot be negative.

Which unit is used to measure Angular Speed of Vane Pump given Theoretical Discharge?

Angular Speed of Vane Pump given Theoretical Discharge is usually measured using the Revolution per Minute[rev/min] for Angular Velocity. Radian per Second[rev/min], Radian per Day[rev/min], Radian per Hour[rev/min] are the few other units in which Angular Speed of Vane Pump given Theoretical Discharge can be measured.

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Angular Speed of Vane Pump given Theoretical Discharge Formula

Angular Speed of Vane Pump given Theoretical Discharge Example

Angular Speed of Vane Pump given Theoretical Discharge Solution

Angular Speed of Vane Pump given Theoretical Discharge Formula Elements

Other formulas in Vane Pumps category

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

FAQs on Angular Speed of Vane Pump given Theoretical Discharge

Variable Name