Torque Given Thickness Of Oil Calculator

Formula Used:

\[ Torque\ Exerted\ on\ Disc = \frac{\pi \times Dynamic\ Viscosity\ Fluid \times Angular\ Velocity \times (Outer\ Radius\ of\ Disc^4 - Inner\ Radius\ of\ Disc^4)}{2 \times Thickness\ of\ Oil \times \sin(Tilt\ Angle)} \]

Dynamic Viscosity Fluid (μ):

Pa·s

Angular Velocity (ω):

rad/s

Outer Radius of Disc (ro):

Inner Radius of Disc (ri):

Thickness of Oil (h):

Tilt Angle (θ):

rad

Torque Exerted on Disc (Td):

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1. What is Torque Exerted on Disc?

Torque exerted on disc is described as the turning effect of force on the axis of rotation. In brief, it is a moment of force that causes rotational motion in mechanical systems involving discs submerged in fluid.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ Td = \frac{\pi \times \mu \times \omega \times (r_o^4 - r_i^4)}{2 \times h \times \sin(\theta)} \]

Where:

\( Td \) — Torque exerted on disc (N·m)
\( \mu \) — Dynamic viscosity of fluid (Pa·s)
\( \omega \) — Angular velocity (rad/s)
\( r_o \) — Outer radius of disc (m)
\( r_i \) — Inner radius of disc (m)
\( h \) — Thickness of oil (m)
\( \theta \) — Tilt angle (rad)
\( \pi \) — Archimedes' constant (≈3.1416)

Explanation: This formula calculates the torque required to rotate a disc submerged in a viscous fluid, accounting for the fluid's resistance and the disc's geometric properties.

3. Importance of Torque Calculation

Details: Accurate torque calculation is crucial for designing mechanical systems involving rotating discs in fluids, such as in bearings, clutches, and fluid coupling devices. It helps in determining power requirements and efficiency.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure viscosity, angular velocity, radii, thickness, and angle are positive values. The inner radius can be zero for solid discs.

5. Frequently Asked Questions (FAQ)

Q1: What is dynamic viscosity?
A: Dynamic viscosity is a measure of a fluid's resistance to flow when an external shear force is applied between its layers.

Q2: Can the inner radius be zero?
A: Yes, for solid discs without a central hole, the inner radius can be set to zero.

Q3: What units should be used for the tilt angle?
A: The tilt angle should be entered in radians. Remember that π radians = 180 degrees.

Q4: What happens if the denominator becomes zero?
A: If either thickness or sin(θ) is zero, the calculation becomes undefined as division by zero is not possible.

Q5: What are typical applications of this calculation?
A: This calculation is commonly used in the design of viscometers, fluid couplings, and various rotating machinery where discs operate in viscous fluids.