Corresponding distance x travelled by Piston Solution

STEP 0: Pre-Calculation Summary
Formula Used
Distance travelled by piston = Radius of crank*(1-cos(Angular Velocity*Time in seconds))
x = r*(1-cos(ω*tsec))
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
Distance travelled by piston - (Measured in Meter) - Distance travelled by piston is defined as the product of radius of crank and cos of product of angular velocity and time, subtracted from 1.
Radius of crank - (Measured in Meter) - Radius of crank is defined as the distance between crank pin and crank center, i.e. half stroke.
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.
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
Radius of crank: 0.09 Meter --> 0.09 Meter No Conversion Required
Angular Velocity: 2.5 Radian per Second --> 2.5 Radian per Second No Conversion Required
Time in seconds: 38 Second --> 38 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
x = r*(1-cos(ω*tsec)) --> 0.09*(1-cos(2.5*38))
Evaluating ... ...
x = 0.0242843795104662
STEP 3: Convert Result to Output's Unit
0.0242843795104662 Meter --> No Conversion Required
FINAL ANSWER
0.0242843795104662 0.024284 Meter <-- Distance travelled by piston
(Calculation completed in 00.004 seconds)

Credits

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

Corresponding distance x travelled by Piston Formula

Distance travelled by piston = Radius of crank*(1-cos(Angular Velocity*Time in seconds))
x = r*(1-cos(ω*tsec))

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 Corresponding distance x travelled by Piston?

Corresponding distance x travelled by Piston calculator uses Distance travelled by piston = Radius of crank*(1-cos(Angular Velocity*Time in seconds)) to calculate the Distance travelled by piston, The corresponding distance x travelled by piston formula is defined as the product of radius of crank and cos of product of angular velocity and time, subtracted from 1. Distance travelled by piston is denoted by x symbol.

How to calculate Corresponding distance x travelled by Piston using this online calculator? To use this online calculator for Corresponding distance x travelled by Piston, enter Radius of crank (r), Angular Velocity (ω) & Time in seconds (tsec) and hit the calculate button. Here is how the Corresponding distance x travelled by Piston calculation can be explained with given input values -> 0.01581 = 0.09*(1-cos(2.5*38)).

FAQ

What is Corresponding distance x travelled by Piston?
The corresponding distance x travelled by piston formula is defined as the product of radius of crank and cos of product of angular velocity and time, subtracted from 1 and is represented as x = r*(1-cos(ω*tsec)) or Distance travelled by piston = Radius of crank*(1-cos(Angular Velocity*Time in seconds)). Radius of crank is defined as the distance between crank pin and crank center, i.e. half stroke, 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 & Time in seconds is what a clock reads, it is a scalar quantity.
How to calculate Corresponding distance x travelled by Piston?
The corresponding distance x travelled by piston formula is defined as the product of radius of crank and cos of product of angular velocity and time, subtracted from 1 is calculated using Distance travelled by piston = Radius of crank*(1-cos(Angular Velocity*Time in seconds)). To calculate Corresponding distance x travelled by Piston, you need Radius of crank (r), Angular Velocity (ω) & Time in seconds (tsec). With our tool, you need to enter the respective value for Radius of crank, Angular Velocity & 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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