Velocity of Piston for Shear Force Resisting Motion of Piston Calculator

Formula Used:

\[ Velocity\ of\ Piston = \frac{Shear\ Force}{\pi \times Dynamic\ Viscosity \times Piston\ Length \times \left(1.5 \times \left(\frac{Diameter\ of\ Piston}{Radial\ Clearance}\right)^2 + 4 \times \left(\frac{Diameter\ of\ Piston}{Radial\ Clearance}\right)\right)} \]

Shear Force (Fs):

Dynamic Viscosity (μ):

Pa·s

Piston Length (LP):

Diameter of Piston (D):

Radial Clearance (CR):

Velocity of Piston:

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1. What is Velocity of Piston for Shear Force Resisting Motion of Piston?

The Velocity of Piston for Shear Force Resisting Motion of Piston is a calculation that determines the speed at which a piston moves when subjected to a shear force that resists its motion, taking into account fluid viscosity, piston dimensions, and clearance.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

\( Shear\ Force \) — Force resisting piston motion (N)
\( \pi \) — Mathematical constant pi (≈3.14159)
\( Dynamic\ Viscosity \) — Fluid viscosity (Pa·s)
\( Piston\ Length \) — Length of piston travel (m)
\( Diameter\ of\ Piston \) — Piston diameter (m)
\( Radial\ Clearance \) — Clearance between piston and cylinder (m)

Explanation: The formula accounts for the relationship between shear force, fluid viscosity, and piston geometry to determine the velocity at which the piston can move against the resisting force.

3. Importance of Piston Velocity Calculation

Details: Accurate piston velocity calculation is crucial for designing hydraulic systems, predicting pump performance, optimizing fluid flow, and ensuring proper operation of reciprocating machinery.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Shear force in Newtons, dynamic viscosity in Pascal-seconds, lengths in meters. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of radial clearance in this calculation?
A: Radial clearance affects the fluid flow resistance around the piston. Smaller clearances increase resistance, requiring more force for the same velocity.

Q2: How does dynamic viscosity affect piston velocity?
A: Higher viscosity fluids create more resistance to piston movement, resulting in lower velocities for the same applied force.

Q3: What are typical values for piston velocity in hydraulic systems?
A: Typical piston velocities range from 0.1 to 10 m/s, depending on the application and system design requirements.

Q4: Can this formula be used for compressible fluids?
A: This formula is primarily designed for incompressible fluids. For compressible fluids, additional factors need to be considered.

Q5: How does piston diameter affect the velocity calculation?
A: Larger piston diameters increase the surface area subject to shear forces, which affects the velocity for a given force input.