Theoretical Volumetric Displacement of External Gear Pump Calculator

✖Width of Rotor is the width of the rotor of a pump.ⓘ Width of Rotor [w]			+10% -10%
✖Outer Diameter of Gear Teeth is the diameter of a circle around the outer surface, or tops of the gear teeth.ⓘ Outer Diameter of Gear Teeth [D_o]			+10% -10%
✖Inner diameter of gear teeth is the diameter of the circle passing along the base of the teeth of a gear.ⓘ Inner Diameter of Gear Teeth [D_i]			+10% -10%

✖Theoretical volumetric displacement in Gear Pump is the amount of liquid displaced per revolution.ⓘ Theoretical Volumetric Displacement of External Gear Pump [V_gp]

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Formula

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Theoretical Volumetric Displacement of External Gear Pump

Formula

`"V"_{"gp"} = pi/4*"w"*("D"_{"o"}^2-"D"_{"i"}^2)`

Example

`"0.020717m³/1"=pi/4*"0.02m"*(("1.15m")^2-("0.06m")^2)`

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Theoretical Volumetric Displacement of External Gear Pump Solution

STEP 0: Pre-Calculation Summary

Formula Used

Theoretical Volumetric Displacement in Gear Pump = pi/4*Width of Rotor*(Outer Diameter of Gear Teeth^2-Inner Diameter of Gear Teeth^2)
V_gp = pi/4*w*(D_o^2-D_i^2)
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Theoretical Volumetric Displacement in Gear Pump - (Measured in Cubic Meter Per Revolution) - Theoretical volumetric displacement in Gear Pump is the amount of liquid displaced per revolution.
Width of Rotor - (Measured in Meter) - Width of Rotor is the width of the rotor of a pump.
Outer Diameter of Gear Teeth - (Measured in Meter) - Outer Diameter of Gear Teeth is the diameter of a circle around the outer surface, or tops of the gear teeth.
Inner Diameter of Gear Teeth - (Measured in Meter) - Inner diameter of gear teeth is the diameter of the circle passing along the base of the teeth of a gear.

STEP 1: Convert Input(s) to Base Unit

Width of Rotor: 0.02 Meter --> 0.02 Meter No Conversion Required
Outer Diameter of Gear Teeth: 1.15 Meter --> 1.15 Meter No Conversion Required
Inner Diameter of Gear Teeth: 0.06 Meter --> 0.06 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_gp = pi/4*w*(D_o^2-D_i^2) --> pi/4*0.02*(1.15^2-0.06^2)

Evaluating ... ...

V_gp = 0.0207172327540979

STEP 3: Convert Result to Output's Unit

0.0207172327540979 Cubic Meter Per Revolution --> No Conversion Required

FINAL ANSWER

0.0207172327540979 ≈ 0.020717 Cubic Meter Per Revolution <-- Theoretical Volumetric Displacement in Gear Pump

(Calculation completed in 00.004 seconds)

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< 12 Gear Pumps Calculators

Theoretical Discharge given Outer and Inner Gear Diameter

Go Theoretical Discharge of Pump in Gear Pump = pi/4*(Outer Diameter of Gear Teeth^2-Inner Diameter of Gear Teeth^2)*Angular Speed of Driving Member in Gear Pump

Width of Rotor given Volumetric Displacement

Go Width of Rotor = (4*Theoretical Volumetric Displacement in Gear Pump)/(pi*(Outer Diameter of Gear Teeth^2-Inner Diameter of Gear Teeth^2))

Theoretical Volumetric Displacement of External Gear Pump

Go Theoretical Volumetric Displacement in Gear Pump = pi/4*Width of Rotor*(Outer Diameter of Gear Teeth^2-Inner Diameter of Gear Teeth^2)

Pump Slippage Percentage

Go Pump Slippage Percentage = ((Theoretical Discharge of Pump in Gear Pump-Actual Discharge of Pump for Gear Pump)/Theoretical Discharge of Pump in Gear Pump)*100

Angular Speed given Theoretical Discharge and Volumetric Displacement

Go Angular Speed of Driving Member in Gear Pump = Theoretical Discharge of Pump in Gear Pump/Theoretical Volumetric Displacement in Gear Pump

Theoretical Discharge of External Gear Pump

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

Volumetric Efficiency of Gear Pumps

Go Volumetric Efficiency of Pump = Actual Discharge of Pump for Gear Pump/Theoretical Discharge of Pump in Gear Pump*100

Actual Discharge given Volumetric Efficiency and Theoretical Discharge

Go Actual Discharge of Pump for Gear Pump = (Volumetric Efficiency of Pump*Theoretical Discharge of Pump in Gear Pump)

Theoretical Discharge given Volumetric Efficiency and Actual Discharge

Go Theoretical Discharge of Pump in Gear Pump = Actual Discharge of Pump for Gear Pump/Volumetric Efficiency of Pump

Theoretical Discharge given Pump Slippage

Go Theoretical Discharge of Pump in Gear Pump = Pump Slippage+Actual Discharge of Pump for Gear Pump

Actual Discharge given Pump Slippage

Go Actual Discharge of Pump for Gear Pump = Theoretical Discharge of Pump in Gear Pump-Pump Slippage

Pump Slippage

Go Pump Slippage = Theoretical Discharge of Pump in Gear Pump-Actual Discharge of Pump for Gear Pump

Theoretical Volumetric Displacement of External Gear Pump Formula

Theoretical Volumetric Displacement in Gear Pump = pi/4*Width of Rotor*(Outer Diameter of Gear Teeth^2-Inner Diameter of Gear Teeth^2)
V_gp = pi/4*w*(D_o^2-D_i^2)

What is theoretical volumetric displacement?

Volumetric displacement or the theoretical volumetric displacement of a positive displacement pump is the amount of liquid pumped in one revolution.

How to Calculate Theoretical Volumetric Displacement of External Gear Pump?

Theoretical Volumetric Displacement of External Gear Pump calculator uses Theoretical Volumetric Displacement in Gear Pump = pi/4*Width of Rotor*(Outer Diameter of Gear Teeth^2-Inner Diameter of Gear Teeth^2) to calculate the Theoretical Volumetric Displacement in Gear Pump, Theoretical Volumetric Displacement of External Gear Pump refers to the volume of fluid that the pump should ideally displace or deliver per revolution of the gears. It is a measure of the pump's capacity and is based on its geometric parameters and rotational speed. Theoretical Volumetric Displacement in Gear Pump is denoted by V_gp symbol.

How to calculate Theoretical Volumetric Displacement of External Gear Pump using this online calculator? To use this online calculator for Theoretical Volumetric Displacement of External Gear Pump, enter Width of Rotor (w), Outer Diameter of Gear Teeth (D_o) & Inner Diameter of Gear Teeth (D_i) and hit the calculate button. Here is how the Theoretical Volumetric Displacement of External Gear Pump calculation can be explained with given input values -> 207.5556 = pi/4*0.02*(1.15^2-0.06^2).

FAQ

What is Theoretical Volumetric Displacement of External Gear Pump?

Theoretical Volumetric Displacement of External Gear Pump refers to the volume of fluid that the pump should ideally displace or deliver per revolution of the gears. It is a measure of the pump's capacity and is based on its geometric parameters and rotational speed and is represented as V_gp = pi/4*w*(D_o^2-D_i^2) or Theoretical Volumetric Displacement in Gear Pump = pi/4*Width of Rotor*(Outer Diameter of Gear Teeth^2-Inner Diameter of Gear Teeth^2). Width of Rotor is the width of the rotor of a pump, Outer Diameter of Gear Teeth is the diameter of a circle around the outer surface, or tops of the gear teeth & Inner diameter of gear teeth is the diameter of the circle passing along the base of the teeth of a gear.

How to calculate Theoretical Volumetric Displacement of External Gear Pump?

Theoretical Volumetric Displacement of External Gear Pump refers to the volume of fluid that the pump should ideally displace or deliver per revolution of the gears. It is a measure of the pump's capacity and is based on its geometric parameters and rotational speed is calculated using Theoretical Volumetric Displacement in Gear Pump = pi/4*Width of Rotor*(Outer Diameter of Gear Teeth^2-Inner Diameter of Gear Teeth^2). To calculate Theoretical Volumetric Displacement of External Gear Pump, you need Width of Rotor (w), Outer Diameter of Gear Teeth (D_o) & Inner Diameter of Gear Teeth (D_i). With our tool, you need to enter the respective value for Width of Rotor, Outer Diameter of Gear Teeth & Inner Diameter of Gear Teeth 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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