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Belt Velocity of V-Belt given Belt Tension in Loose Side Formula

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Belt Velocity is defined as the velocity of the belt used in a belt drive. Check FAQs

v b = \sqrt{\frac{P 1 - (e^{μ \cdot \frac{α}{\sin (\frac{θ}{2})}}) \cdot P 2}{m v \cdot (1 - (e^{μ \cdot \frac{α}{\sin (\frac{θ}{2})}}))}}

v_b - Belt Velocity?P₁ - Belt Tension on Tight Side?μ - Coefficient of Friction for Belt Drive?α - Wrap Angle on Pulley?θ - V Belt Angle?P₂ - Belt Tension on Loose Side?m_v - Mass of Meter Length of V Belt?

Belt Velocity of V-Belt given Belt Tension in Loose Side Example

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Here is how the Belt Velocity of V-Belt given Belt Tension in Loose Side equation looks like with Values.

Here is how the Belt Velocity of V-Belt given Belt Tension in Loose Side equation looks like with Units.

Here is how the Belt Velocity of V-Belt given Belt Tension in Loose Side equation looks like.

25.8038 = \sqrt{\frac{800 - (e^{0.35 \cdot \frac{160.2}{\sin (\frac{62}{2})}}) \cdot 550}{0.76 \cdot (1 - (e^{0.35 \cdot \frac{160.2}{\sin (\frac{62}{2})}}))}}

25.8038m/s = \sqrt{\frac{800N - (e^{0.35 \cdot \frac{160.2°}{\sin (\frac{62°}{2})}}) \cdot 550N}{0.76kg/m \cdot (1 - (e^{0.35 \cdot \frac{160.2°}{\sin (\frac{62°}{2})}}))}}

25.8038 = \sqrt{\frac{800 - (e^{0.35 \cdot \frac{160.2}{\sin (\frac{62}{2})}}) \cdot 550}{0.76 \cdot (1 - (e^{0.35 \cdot \frac{160.2}{\sin (\frac{62}{2})}}))}}

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Belt Velocity of V-Belt given Belt Tension in Loose Side Solution

Follow our step by step solution on how to calculate Belt Velocity of V-Belt given Belt Tension in Loose Side?

FIRST Step Consider the formula

v b = \sqrt{\frac{P 1 - (e^{μ \cdot \frac{α}{\sin (\frac{θ}{2})}}) \cdot P 2}{m v \cdot (1 - (e^{μ \cdot \frac{α}{\sin (\frac{θ}{2})}}))}}

Next Step Substitute values of Variables

∴

v b = \sqrt{\frac{800N - (e^{0.35 \cdot \frac{160.2°}{\sin (\frac{62°}{2})}}) \cdot 550N}{0.76kg/m \cdot (1 - (e^{0.35 \cdot \frac{160.2°}{\sin (\frac{62°}{2})}}))}}

Next Step Convert Units

∴

v b = \sqrt{\frac{800N - (e^{0.35 \cdot \frac{2.796rad}{\sin (\frac{1.0821rad}{2})}}) \cdot 550N}{0.76kg/m \cdot (1 - (e^{0.35 \cdot \frac{2.796rad}{\sin (\frac{1.0821rad}{2})}}))}}

Next Step Prepare to Evaluate

∴

v b = \sqrt{\frac{800 - (e^{0.35 \cdot \frac{2.796}{\sin (\frac{1.0821}{2})}}) \cdot 550}{0.76 \cdot (1 - (e^{0.35 \cdot \frac{2.796}{\sin (\frac{1.0821}{2})}}))}}

Next Step Evaluate

∴

v b = 25.8037873000393m/s

LAST Step Rounding Answer

∴

v b = 25.8038m/s

Belt Velocity of V-Belt given Belt Tension in Loose Side Formula Elements

Variables

Functions

Belt Velocity

Belt Velocity is defined as the velocity of the belt used in a belt drive.

Symbol: v_b

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Belt Velocity

Belt Tension on Tight Side

Belt Tension on Tight Side is defined as the belt's tension on the belt's tight side.

Symbol: P₁

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Belt Tension on Tight Side

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.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of Friction for Belt Drive

Wrap Angle on Pulley

Wrap Angle on Pulley is the angle between the run-up and run-off of the belt on the pulley.

Symbol: α

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Wrap Angle on Pulley

V Belt Angle

V Belt Angle is defined as the angle included between the side faces of the V cross-section belt.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find V Belt Angle

Belt Tension on Loose Side

Belt Tension on Loose Side is defined as the belt's tension on the belt's loose side.

Symbol: P₂

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Belt Tension on Loose Side

Mass of Meter Length of V Belt

Mass of Meter Length of V Belt is the mass of 1-meter length of the belt simply mass per unit length of the belt.

Symbol: m_v

Measurement: Linear Mass DensityUnit: kg/m

Note: Value should be greater than 0.

Formulas to find Mass of Meter Length of V Belt

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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.

Syntax: sqrt(Number)

Other formulas in V Belt Characteristics and Parameters category

Go Belt Tension in Loose Side of V-Belt

P 2 = \frac{P 1 - m v \cdot {v b}^{2}}{e^{μ} \cdot \frac{α}{\sin (\frac{θ}{2})}} + m v \cdot {v b}^{2}

Go Belt Tension in Tight Side of V-Belt

P 1 = (e^{μ} \cdot \frac{α}{\sin (\frac{θ}{2})}) \cdot (P 2 - m v \cdot {v b}^{2}) + m v \cdot {v b}^{2}

How to Evaluate Belt Velocity of V-Belt given Belt Tension in Loose Side?

Belt Velocity of V-Belt given Belt Tension in Loose Side evaluator uses Belt Velocity = sqrt((Belt Tension on Tight Side-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2)))*Belt Tension on Loose Side)/(Mass of Meter Length of V Belt*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2)))))) to evaluate the Belt Velocity, The Belt Velocity of V-Belt given Belt Tension in Loose Side formula is defined as a method to determine the speed at which a V-belt operates, considering the tension on its loose side and the mechanical properties involved in its movement. Belt Velocity is denoted by v_b symbol.

How to evaluate Belt Velocity of V-Belt given Belt Tension in Loose Side using this online evaluator? To use this online evaluator for Belt Velocity of V-Belt given Belt Tension in Loose Side, enter Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), V Belt Angle (θ), Belt Tension on Loose Side (P₂) & Mass of Meter Length of V Belt (m_v) and hit the calculate button.

FAQs on Belt Velocity of V-Belt given Belt Tension in Loose Side

What is the formula to find Belt Velocity of V-Belt given Belt Tension in Loose Side?

The formula of Belt Velocity of V-Belt given Belt Tension in Loose Side is expressed as Belt Velocity = sqrt((Belt Tension on Tight Side-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2)))*Belt Tension on Loose Side)/(Mass of Meter Length of V Belt*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2)))))). Here is an example- 25.80379 = sqrt((800-(e^(0.35*2.79601746169439/sin(1.08210413623628/2)))*550)/(0.76*(1-(e^(0.35*2.79601746169439/sin(1.08210413623628/2)))))).

How to calculate Belt Velocity of V-Belt given Belt Tension in Loose Side?

With Belt Tension on Tight Side (P₁), Coefficient of Friction for Belt Drive (μ), Wrap Angle on Pulley (α), V Belt Angle (θ), Belt Tension on Loose Side (P₂) & Mass of Meter Length of V Belt (m_v) we can find Belt Velocity of V-Belt given Belt Tension in Loose Side using the formula - Belt Velocity = sqrt((Belt Tension on Tight Side-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2)))*Belt Tension on Loose Side)/(Mass of Meter Length of V Belt*(1-(e^(Coefficient of Friction for Belt Drive*Wrap Angle on Pulley/sin(V Belt Angle/2)))))). This formula also uses Sine (sin), Square Root (sqrt) function(s).

Can the Belt Velocity of V-Belt given Belt Tension in Loose Side be negative?

No, the Belt Velocity of V-Belt given Belt Tension in Loose Side, measured in Speed cannot be negative.

Which unit is used to measure Belt Velocity of V-Belt given Belt Tension in Loose Side?

Belt Velocity of V-Belt given Belt Tension in Loose Side is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which Belt Velocity of V-Belt given Belt Tension in Loose Side can be measured.

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Belt Velocity of V-Belt given Belt Tension in Loose Side Formula

Belt Velocity of V-Belt given Belt Tension in Loose Side Example

Belt Velocity of V-Belt given Belt Tension in Loose Side Solution

Belt Velocity of V-Belt given Belt Tension in Loose Side Formula Elements

Other formulas in V Belt Characteristics and Parameters category

How to Evaluate Belt Velocity of V-Belt given Belt Tension in Loose Side?

FAQs on Belt Velocity of V-Belt given Belt Tension in Loose Side

Variable Name