Velocity of belt given tension of belt in tight side Calculator

✖Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley.ⓘ Coefficient of Friction for Belt Drive [μ]			+10% -10%
✖Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley.ⓘ Wrap Angle on Pulley [α]			+10% -10%
✖Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side.ⓘ Belt Tension on Loose Side [P₂]			+10% -10%
✖Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side.ⓘ Belt Tension on Tight Side [P₁]			+10% -10%
✖Mass of Meter Length of Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.ⓘ Mass of Meter Length of Belt [m]			+10% -10%

✖Belt Velocity is defined as the velocity of the belt used in a belt drive.ⓘ Velocity of belt given tension of belt in tight side [v_b]

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Formula

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Velocity of belt given tension of belt in tight side

Formula

`"v"_{"b"} = sqrt((((e^("μ"*"α"))*"P"_{"2"})-"P"_{"1"})/("m"*((e^("μ"*"α"))-1)))`

Example

`"25.80262m/s"=sqrt((((e^("0.35"*"160.2°"))*"550N")-"800N")/("0.6kg/m"*((e^("0.35"*"160.2°"))-1)))`

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Velocity of belt given tension of belt in tight side Solution

STEP 0: Pre-Calculation Summary

Formula Used

Belt Velocity = sqrt((((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side)-Belt Tension on Tight Side)/(Mass of Meter Length of Belt*((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))-1)))
v_b = sqrt((((e^(μ*α))*P₂)-P₁)/(m*((e^(μ*α))-1)))
This formula uses 1 Constants, 1 Functions, 6 Variables

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Belt Velocity - (Measured in Meter per Second) - Belt Velocity is defined as the velocity of the belt used in a belt drive.
Coefficient of Friction for Belt Drive - Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley.
Wrap Angle on Pulley - (Measured in Radian) - Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley.
Belt Tension on Loose Side - (Measured in Newton) - Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side.
Belt Tension on Tight Side - (Measured in Newton) - Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side.
Mass of Meter Length of Belt - (Measured in Kilogram per Meter) - Mass of Meter Length of Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.

STEP 1: Convert Input(s) to Base Unit

Coefficient of Friction for Belt Drive: 0.35 --> No Conversion Required
Wrap Angle on Pulley: 160.2 Degree --> 2.79601746169439 Radian (Check conversion here)
Belt Tension on Loose Side: 550 Newton --> 550 Newton No Conversion Required
Belt Tension on Tight Side: 800 Newton --> 800 Newton No Conversion Required
Mass of Meter Length of Belt: 0.6 Kilogram per Meter --> 0.6 Kilogram per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_b = sqrt((((e^(μ*α))*P₂)-P₁)/(m*((e^(μ*α))-1))) --> sqrt((((e^(0.35*2.79601746169439))*550)-800)/(0.6*((e^(0.35*2.79601746169439))-1)))

Evaluating ... ...

v_b = 25.8026206130076

STEP 3: Convert Result to Output's Unit

25.8026206130076 Meter per Second --> No Conversion Required

FINAL ANSWER

25.8026206130076 ≈ 25.80262 Meter per Second <-- Belt Velocity

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

Kethavath Srinath has created this Calculator and 1000+ more calculators!

Verified by Urvi Rathod

Vishwakarma Government Engineering College (VGEC), Ahmedabad

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< 15 Introduction of Belt Drives Calculators

Velocity of belt given tension of belt in tight side

Go Belt Velocity = sqrt((((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side)-Belt Tension on Tight Side)/(Mass of Meter Length of Belt*((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))-1)))

Angle of Wrap given Belt Tension in Tight Side

Go Wrap Angle on Pulley = ln((Belt Tension on Tight Side-Mass of Meter Length of Belt*Belt Velocity^2)/(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))/Coefficient of Friction for Belt Drive

Mass per unit length of belt

Go Mass of Meter Length of Belt = (Belt Tension on Tight Side-((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side))/((Belt Velocity^2)*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))))

Coefficient of Friction in between Surfaces given Belt Tension in Tight Side

Go Coefficient of Friction for Belt Drive = ln((Belt Tension on Tight Side-Mass of Meter Length of Belt*Belt Velocity^2)/(Belt Tension on Loose Side-Mass of Meter Length of Belt*Belt Velocity^2))/Wrap Angle on Pulley

Belt Tension in Loose Side of Belt given Tension in Tight Side

Go Belt Tension on Loose Side = ((Belt Tension on Tight Side-(Mass of Meter Length of Belt*Belt Velocity^2))/(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley)))+(Mass of Meter Length of Belt*Belt Velocity^2)

Belt tension in tight side

Go Belt Tension on Tight Side = ((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*(Belt Tension on Loose Side-(Mass of Meter Length of Belt*Belt Velocity^2)))+(Mass of Meter Length of Belt*Belt Velocity^2)

Length of Belt

Go Belt Length = (2*Centre Distance between Pulleys)+(pi*(Diameter of Big Pulley+Diameter of Small Pulley)/2)+(((Diameter of Big Pulley-Diameter of Small Pulley)^2)/(4*Centre Distance between Pulleys))

Wrap Angle for Small Pulley

Go Wrap Angle on Small Pulley = 3.14-(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))

Center Distance from Small Pulley to Big Pulley given Wrap Angle of Small Pulley

Go Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((3.14-Wrap Angle on Small Pulley)/2))

Wrap Angle for Big Pulley

Go Wrap Angle on Big Pulley = 3.14+(2*(asin((Diameter of Big Pulley-Diameter of Small Pulley)/(2*Centre Distance between Pulleys))))

Center Distance from Small Pulley to Big Pulley given Wrap Angle of Big Pulley

Go Centre Distance between Pulleys = (Diameter of Big Pulley-Diameter of Small Pulley)/(2*sin((Wrap Angle on Big Pulley-3.14)/2))

Diameter of Small Pulley given Wrap Angle of Small Pulley

Go Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Big Pulley given Wrap Angle of Small Pulley

Go Diameter of Big Pulley = Diameter of Small Pulley+(2*Centre Distance between Pulleys*sin((3.14-Wrap Angle on Small Pulley)/2))

Diameter of Small Pulley given Wrap Angle of Big Pulley

Go Diameter of Small Pulley = Diameter of Big Pulley-(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2))

Diameter of Big Pulley given Wrap Angle for Big Pulley

Go Diameter of Big Pulley = Diameter of Small Pulley+(2*Centre Distance between Pulleys*sin((Wrap Angle on Big Pulley-3.14)/2))

Velocity of belt given tension of belt in tight side Formula

Types of Belt Drives?

There are five different kinds of belt drive that can be found and those are:
Open belt drive.
Closed or crossed belt drive.
Fast and loose cone pulley.
Stepped cone pulley.
Jockey pulley drive.

How to Calculate Velocity of belt given tension of belt in tight side?

Velocity of belt given tension of belt in tight side calculator uses Belt Velocity = sqrt((((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side)-Belt Tension on Tight Side)/(Mass of Meter Length of Belt*((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))-1))) to calculate the Belt Velocity, Velocity of belt given tension of belt in tight side is a measure of the rotational speed of the belt at which the rotational force is being transferred from one pulley to another. Belt Velocity is denoted by v_b symbol.

How to calculate Velocity of belt given tension of belt in tight side using this online calculator? To use this online calculator for Velocity of belt given tension of belt in tight side, enter Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), Belt Tension on Loose Side (P₂), Belt Tension on Tight Side (P₁) & Mass of Meter Length of Belt (m) and hit the calculate button. Here is how the Velocity of belt given tension of belt in tight side calculation can be explained with given input values -> 25.80262 = sqrt((((e^(0.35*2.79601746169439))*550)-800)/(0.6*((e^(0.35*2.79601746169439))-1))).

FAQ

What is Velocity of belt given tension of belt in tight side?

Velocity of belt given tension of belt in tight side is a measure of the rotational speed of the belt at which the rotational force is being transferred from one pulley to another and is represented as v_b = sqrt((((e^(μ*α))*P₂)-P₁)/(m*((e^(μ*α))-1))) or Belt Velocity = sqrt((((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side)-Belt Tension on Tight Side)/(Mass of Meter Length of Belt*((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))-1))). Coefficient of Friction for Belt Drive is the ratio defining the force that resists the motion of the belt over the pulley, Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley, Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side, Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side & Mass of Meter Length of Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.

How to calculate Velocity of belt given tension of belt in tight side?

Velocity of belt given tension of belt in tight side is a measure of the rotational speed of the belt at which the rotational force is being transferred from one pulley to another is calculated using Belt Velocity = sqrt((((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))*Belt Tension on Loose Side)-Belt Tension on Tight Side)/(Mass of Meter Length of Belt*((e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley))-1))). To calculate Velocity of belt given tension of belt in tight side, you need Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), Belt Tension on Loose Side (P₂), Belt Tension on Tight Side (P₁) & Mass of Meter Length of Belt (m). With our tool, you need to enter the respective value for Coefficient of Friction for Belt Drive, Wrap Angle on Pulley, Belt Tension on Loose Side, Belt Tension on Tight Side & Mass of Meter Length of Belt 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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