Theoretical Discharge given Outer and Inner Gear Diameter Calculator

✖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%
✖The Angular Speed of Driving Member in Gear Pump is the rate of change of angular position of the driving or the input member.ⓘ Angular Speed of Driving Member in Gear Pump [n₁]			+10% -10%

✖Theoretical Discharge of Pump in Gear Pump is the volume of liquid pumped out in unit time.ⓘ Theoretical Discharge given Outer and Inner Gear Diameter [Q_gp]

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Formula

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Theoretical Discharge given Outer and Inner Gear Diameter

Formula

`"Q"_{"gp"} = pi/4*("D"_{"o"}^2-"D"_{"i"}^2)*"n"_{"1"}`

Example

`"28.06795m³/s"=pi/4*(("1.15m")^2-("0.06m")^2)*"258.75rev/min"`

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Theoretical Discharge given Outer and Inner Gear Diameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
Q_gp = pi/4*(D_o^2-D_i^2)*n₁
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Theoretical Discharge of Pump in Gear Pump - (Measured in Cubic Meter per Second) - Theoretical Discharge of Pump in Gear Pump is the volume of liquid pumped out in unit time.
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.
Angular Speed of Driving Member in Gear Pump - (Measured in Radian per Second) - The Angular Speed of Driving Member in Gear Pump is the rate of change of angular position of the driving or the input member.

STEP 1: Convert Input(s) to Base Unit

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
Angular Speed of Driving Member in Gear Pump: 258.75 Revolution per Minute --> 27.0962366358321 Radian per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_gp = pi/4*(D_o^2-D_i^2)*n₁ --> pi/4*(1.15^2-0.06^2)*27.0962366358321

Evaluating ... ...

Q_gp = 28.0679520572324

STEP 3: Convert Result to Output's Unit

28.0679520572324 Cubic Meter per Second --> No Conversion Required

FINAL ANSWER

28.0679520572324 ≈ 28.06795 Cubic Meter per Second <-- Theoretical Discharge of Pump 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 Discharge given Outer and Inner Gear Diameter Formula

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
Q_gp = pi/4*(D_o^2-D_i^2)*n₁

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 Theoretical Discharge given Outer and Inner Gear Diameter?

Theoretical Discharge given Outer and Inner Gear Diameter calculator uses 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 to calculate the Theoretical Discharge of Pump in Gear Pump, Theoretical Discharge given Outer and Inner Gear Diameter refers to the ideal or calculated flow rate that the pump should deliver under ideal conditions. It is typically determined based on the pump's design parameters and operating characteristics. Theoretical Discharge of Pump in Gear Pump is denoted by Q_gp symbol.

How to calculate Theoretical Discharge given Outer and Inner Gear Diameter using this online calculator? To use this online calculator for Theoretical Discharge given Outer and Inner Gear Diameter, enter Outer Diameter of Gear Teeth (D_o), Inner Diameter of Gear Teeth (D_i) & Angular Speed of Driving Member in Gear Pump (n₁) and hit the calculate button. Here is how the Theoretical Discharge given Outer and Inner Gear Diameter calculation can be explained with given input values -> 28.06795 = pi/4*(1.15^2-0.06^2)*27.0962366358321.

FAQ

What is Theoretical Discharge given Outer and Inner Gear Diameter?

Theoretical Discharge given Outer and Inner Gear Diameter refers to the ideal or calculated flow rate that the pump should deliver under ideal conditions. It is typically determined based on the pump's design parameters and operating characteristics and is represented as Q_gp = pi/4*(D_o^2-D_i^2)*n₁ or 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. 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 & The Angular Speed of Driving Member in Gear Pump is the rate of change of angular position of the driving or the input member.

How to calculate Theoretical Discharge given Outer and Inner Gear Diameter?

Theoretical Discharge given Outer and Inner Gear Diameter refers to the ideal or calculated flow rate that the pump should deliver under ideal conditions. It is typically determined based on the pump's design parameters and operating characteristics is calculated using 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. To calculate Theoretical Discharge given Outer and Inner Gear Diameter, you need Outer Diameter of Gear Teeth (D_o), Inner Diameter of Gear Teeth (D_i) & Angular Speed of Driving Member in Gear Pump (n₁). With our tool, you need to enter the respective value for Outer Diameter of Gear Teeth, Inner Diameter of Gear Teeth & Angular Speed of Driving Member in Gear Pump and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Theoretical Discharge of Pump in Gear Pump?

In this formula, Theoretical Discharge of Pump in Gear Pump uses Outer Diameter of Gear Teeth, Inner Diameter of Gear Teeth & Angular Speed of Driving Member in Gear Pump. We can use 3 other way(s) to calculate the same, which is/are as follows -

Theoretical Discharge of Pump in Gear Pump = Theoretical Volumetric Displacement in Gear Pump*Angular Speed of Driving Member in Gear Pump
Theoretical Discharge of Pump in Gear Pump = Actual Discharge of Pump for Gear Pump/Volumetric Efficiency of Pump
Theoretical Discharge of Pump in Gear Pump = Pump Slippage+Actual Discharge of Pump for Gear Pump

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