Acceleration of Piston Calculator

✖The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.ⓘ Angular Velocity [ω]			+10% -10%
✖Radius of crank is defined as the distance between crank pin and crank center, i.e. half stroke.ⓘ Radius of crank [r]			+10% -10%
✖Time in seconds is what a clock reads, it is a scalar quantity.ⓘ Time in seconds [t_sec]			+10% -10%

✖Acceleration of piston in reciprocating pumps is defined as the product of cos of angular velocity and time, radius of crank and angular velocity squared.ⓘ Acceleration of Piston [a_p]

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Formula

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Acceleration of Piston

Formula

`"a"_{"p"} = ("ω"^2)*"r"*cos("ω"*"t"_{"sec"})`

Example

`"0.410723m/s²"=(("2.5rad/s")^2)*"0.09m"*cos("2.5rad/s"*"38s")`

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Acceleration of Piston Solution

STEP 0: Pre-Calculation Summary

Formula Used

Acceleration of piston = (Angular Velocity^2)*Radius of crank*cos(Angular Velocity*Time in seconds)
a_p = (ω^2)*r*cos(ω*t_sec)
This formula uses 1 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Acceleration of piston - (Measured in Meter per Square Second) - Acceleration of piston in reciprocating pumps is defined as the product of cos of angular velocity and time, radius of crank and angular velocity squared.
Angular Velocity - (Measured in Radian per Second) - The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Radius of crank - (Measured in Meter) - Radius of crank is defined as the distance between crank pin and crank center, i.e. half stroke.
Time in seconds - (Measured in Second) - Time in seconds is what a clock reads, it is a scalar quantity.

STEP 1: Convert Input(s) to Base Unit

Angular Velocity: 2.5 Radian per Second --> 2.5 Radian per Second No Conversion Required
Radius of crank: 0.09 Meter --> 0.09 Meter No Conversion Required
Time in seconds: 38 Second --> 38 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a_p = (ω^2)*r*cos(ω*t_sec) --> (2.5^2)*0.09*cos(2.5*38)

Evaluating ... ...

a_p = 0.410722628059586

STEP 3: Convert Result to Output's Unit

0.410722628059586 Meter per Square Second --> No Conversion Required

FINAL ANSWER

0.410722628059586 ≈ 0.410723 Meter per Square Second <-- Acceleration of piston

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Fluid Machinery » Reciprocating Pumps » Fluid Parameters » Acceleration of Piston

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Created by Sagar S Kulkarni

Dayananda Sagar College of Engineering (DSCE), Bengaluru

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< 13 Fluid Parameters Calculators

Intensity of pressure due to acceleration

Go Pressure = Density*Length of Pipe 1*(Area of cylinder/Area of pipe)*Angular Velocity^2*Radius of crank*cos(Angle turned by crank)

Power Required to Drive Pump

Go Power = Specific Weight*Area of Piston*Length of Stroke*Speed*(Height of centre of cylinder+Height to which liquid is raised)/60

Darcy-Weisbach equation

Go Head loss due to friction = (4*Coefficient of Friction*Length of Pipe 1*Velocity of Liquid^2)/(Diameter of delivery pipe*2*[g])

Acceleration of Piston

Go Acceleration of piston = (Angular Velocity^2)*Radius of crank*cos(Angular Velocity*Time in seconds)

Velocity of Piston

Go Velocity of Piston = Angular Velocity*Radius of crank*sin(Angular Velocity*Time in seconds)

Corresponding distance x travelled by Piston

Go Distance travelled by piston = Radius of crank*(1-cos(Angular Velocity*Time in seconds))

Angle Turned by Crank in Time t

Go Angle turned by crank = 2*pi*(Speed/60)*Time in seconds

Resultant Force on body moving in Fluid with certain Density

Go Resultant Force = sqrt(Drag Force^2+Lift Force^2)

Slip percentage

Go Slip Percentage = (1-(Actual Discharge/Theoretical Discharge of Pump))*100

Cross sectional area of piston given volume of liquid

Go Area of Piston = Volume of Liquid sucked/Length of Stroke

Length of Stroke given Volume of Liquid

Go Length of Stroke = Volume of Liquid sucked/Area of Piston

Slip of Pump

Go Pump Slippage = Theoretical Discharge-Actual Discharge

Slip Percentage given Coefficient of Discharge

Go Slip Percentage = (1-Coefficient of Discharge)*100

Acceleration of Piston Formula

Acceleration of piston = (Angular Velocity^2)*Radius of crank*cos(Angular Velocity*Time in seconds)
a_p = (ω^2)*r*cos(ω*t_sec)

What are reciprocating pumps?

The reciprocating pump is a positive displacement pump as it sucks and raises the liquid by actually displacing it with a piston/plunger that executes a reciprocating motion in a closely fitting cylinder. The amount of liquid pumped is equal to the volume displaced by the piston.

How to Calculate Acceleration of Piston?

Acceleration of Piston calculator uses Acceleration of piston = (Angular Velocity^2)*Radius of crank*cos(Angular Velocity*Time in seconds) to calculate the Acceleration of piston, The Acceleration of Piston formula is defined as the product of cos of angular velocity and time, radius of crank and angular velocity squared. Acceleration of piston is denoted by a_p symbol.

How to calculate Acceleration of Piston using this online calculator? To use this online calculator for Acceleration of Piston, enter Angular Velocity (ω), Radius of crank (r) & Time in seconds (t_sec) and hit the calculate button. Here is how the Acceleration of Piston calculation can be explained with given input values -> 0.296759 = (2.5^2)*0.09*cos(2.5*38).

FAQ

What is Acceleration of Piston?

The Acceleration of Piston formula is defined as the product of cos of angular velocity and time, radius of crank and angular velocity squared and is represented as a_p = (ω^2)*r*cos(ω*t_sec) or Acceleration of piston = (Angular Velocity^2)*Radius of crank*cos(Angular Velocity*Time in seconds). The Angular Velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time, Radius of crank is defined as the distance between crank pin and crank center, i.e. half stroke & Time in seconds is what a clock reads, it is a scalar quantity.

How to calculate Acceleration of Piston?

The Acceleration of Piston formula is defined as the product of cos of angular velocity and time, radius of crank and angular velocity squared is calculated using Acceleration of piston = (Angular Velocity^2)*Radius of crank*cos(Angular Velocity*Time in seconds). To calculate Acceleration of Piston, you need Angular Velocity (ω), Radius of crank (r) & Time in seconds (t_sec). With our tool, you need to enter the respective value for Angular Velocity, Radius of crank & Time in seconds 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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