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Theoretical Discharge given Outer and Inner Gear Diameter Formula

GoTheoretical Discharge of External Gear Pump Formula

GoTheoretical Discharge given Volumetric Efficiency and Actual Discharge Formula

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Theoretical Discharge of Pump in Gear Pump is the volume of liquid pumped out in unit time. Check FAQs

Q gp = \frac{π}{4} \cdot ({D o}^{2} - {D i}^{2}) \cdot n 1

Q_gp - Theoretical Discharge of Pump in Gear Pump?D_o - Outer Diameter of Gear Teeth?D_i - Inner Diameter of Gear Teeth?n₁ - Angular Speed of Driving Member in Gear Pump?π - Archimedes' constant?

Theoretical Discharge given Outer and Inner Gear Diameter Example

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Here is how the Theoretical Discharge given Outer and Inner Gear Diameter equation looks like with Values.

Here is how the Theoretical Discharge given Outer and Inner Gear Diameter equation looks like with Units.

Here is how the Theoretical Discharge given Outer and Inner Gear Diameter equation looks like.

28.068 = \frac{3.1416}{4} \cdot ({1.15}^{2} - {0.06}^{2}) \cdot 258.75

28.068m³/s = \frac{3.1416}{4} \cdot ({1.15m}^{2} - {0.06m}^{2}) \cdot 258.75rev/min

28.068 = \frac{3.1416}{4} \cdot ({1.15}^{2} - {0.06}^{2}) \cdot 258.75

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Theoretical Discharge given Outer and Inner Gear Diameter Solution

Follow our step by step solution on how to calculate Theoretical Discharge given Outer and Inner Gear Diameter?

FIRST Step Consider the formula

Q gp = \frac{π}{4} \cdot ({D o}^{2} - {D i}^{2}) \cdot n 1

Next Step Substitute values of Variables

∴

Q gp = \frac{π}{4} \cdot ({1.15m}^{2} - {0.06m}^{2}) \cdot 258.75rev/min

Next Step Substitute values of Constants

∴

Q gp = \frac{3.1416}{4} \cdot ({1.15m}^{2} - {0.06m}^{2}) \cdot 258.75rev/min

Next Step Convert Units

∴

Q gp = \frac{3.1416}{4} \cdot ({1.15m}^{2} - {0.06m}^{2}) \cdot 27.0962rad/s

Next Step Prepare to Evaluate

∴

Q gp = \frac{3.1416}{4} \cdot ({1.15}^{2} - {0.06}^{2}) \cdot 27.0962

Next Step Evaluate

∴

Q gp = 28.0679520572324m³/s

LAST Step Rounding Answer

∴

Q gp = 28.068m³/s

Theoretical Discharge given Outer and Inner Gear Diameter Formula Elements

Variables

Constants

Theoretical Discharge of Pump in Gear Pump

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

Symbol: Q_gp

Measurement: Volumetric Flow RateUnit: m³/s

Note: Value should be greater than 0.

Formulas to find Theoretical Discharge of Pump in Gear Pump

Outer Diameter of Gear Teeth

Outer Diameter of Gear Teeth is the diameter of a circle around the outer surface, or tops of the gear teeth.

Symbol: D_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Diameter of Gear Teeth

Inner Diameter of Gear Teeth

Inner diameter of gear teeth is the diameter of the circle passing along the base of the teeth of a gear.

Symbol: D_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Diameter of Gear Teeth

Angular Speed of Driving Member in Gear Pump

The Angular Speed of Driving Member in Gear Pump 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 in Gear Pump

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 to find Theoretical Discharge of Pump in Gear Pump

Go Theoretical Discharge of External Gear Pump

Q gp = V gp \cdot n 1

Go Theoretical Discharge given Volumetric Efficiency and Actual Discharge

Q gp = \frac{Q ga}{η v}

Go Theoretical Discharge given Pump Slippage

Q gp = S + Q ga

Other formulas in Gear Pumps category

Go Theoretical Volumetric Displacement of External Gear Pump

V gp = \frac{π}{4} \cdot w \cdot ({D o}^{2} - {D i}^{2})

Go Volumetric Efficiency of Gear Pumps

η v = \frac{Q ga}{Q gp} \cdot 100

Go Pump Slippage

S = Q gp - Q ga

Go Pump Slippage Percentage

%S = (\frac{Q gp - Q ga}{Q gp}) \cdot 100

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

Theoretical Discharge given Outer and Inner Gear Diameter evaluator 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 evaluate the Theoretical Discharge of Pump in Gear Pump, Theoretical Discharge given Outer and Inner Gear Diameter formula is defined as a measure of the volumetric flow rate of a hydraulic pump, which is a critical parameter in determining the pump's performance and efficiency in various industrial applications, particularly in hydraulic systems. Theoretical Discharge of Pump in Gear Pump is denoted by Q_gp symbol.

How to evaluate Theoretical Discharge given Outer and Inner Gear Diameter using this online evaluator? To use this online evaluator 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.

FAQs on Theoretical Discharge given Outer and Inner Gear Diameter

What is the formula to find Theoretical Discharge given Outer and Inner Gear Diameter?

The formula of Theoretical Discharge given Outer and Inner Gear Diameter is expressed as 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. Here is an example- 28.06795 = pi/4*(1.15^2-0.06^2)*27.0962366358321.

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

With Outer Diameter of Gear Teeth (D_o), Inner Diameter of Gear Teeth (D_i) & Angular Speed of Driving Member in Gear Pump (n₁) we can find Theoretical Discharge given Outer and Inner Gear Diameter using the 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. This formula also uses Archimedes' constant .

What are the other ways to Calculate Theoretical Discharge of Pump in Gear Pump?

Here are the different ways to Calculate Theoretical Discharge of Pump in Gear Pump-

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

Can the Theoretical Discharge given Outer and Inner Gear Diameter be negative?

No, the Theoretical Discharge given Outer and Inner Gear Diameter, measured in Volumetric Flow Rate cannot be negative.

Which unit is used to measure Theoretical Discharge given Outer and Inner Gear Diameter?

Theoretical Discharge given Outer and Inner Gear Diameter is usually measured using the Cubic Meter per Second[m³/s] for Volumetric Flow Rate. Cubic Meter per Day[m³/s], Cubic Meter per Hour[m³/s], Cubic Meter per Minute[m³/s] are the few other units in which Theoretical Discharge given Outer and Inner Gear Diameter can be measured.

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Theoretical Discharge given Outer and Inner Gear Diameter Formula

​GoTheoretical Discharge of External Gear Pump Formula

​GoTheoretical Discharge given Volumetric Efficiency and Actual Discharge Formula

Theoretical Discharge given Outer and Inner Gear Diameter Example

Theoretical Discharge given Outer and Inner Gear Diameter Solution

Theoretical Discharge given Outer and Inner Gear Diameter Formula Elements

Other Formulas to find Theoretical Discharge of Pump in Gear Pump

Other formulas in Gear Pumps category

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

FAQs on Theoretical Discharge given Outer and Inner Gear Diameter

Variable Name

GoTheoretical Discharge of External Gear Pump Formula

GoTheoretical Discharge given Volumetric Efficiency and Actual Discharge Formula