Velocity Of Liquid In Pipe Calculator

Formula Used:

\[ v_{liquid} = \frac{A}{a} \times \omega \times r \times \sin(\omega \times t_{sec}) \]

Area of Cylinder (A):

m²

Area of Pipe (a):

m²

Angular Velocity (ω):

rad/s

Radius of Crank (r):

Time in Seconds (t):

Velocity of Liquid (v):

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1. What is the Velocity of Liquid in Pipe Formula?

The Velocity of Liquid in Pipe formula calculates the instantaneous velocity of liquid flowing through a pipe system that includes a cylinder and crank mechanism. It accounts for the relationship between cylinder area, pipe area, angular velocity, crank radius, and time.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ v_{liquid} = \frac{A}{a} \times \omega \times r \times \sin(\omega \times t_{sec}) \]

Where:

\( v_{liquid} \) — Velocity of liquid in pipe (m/s)
\( A \) — Area of cylinder (m²)
\( a \) — Area of pipe (m²)
\( \omega \) — Angular velocity (rad/s)
\( r \) — Radius of crank (m)
\( t_{sec} \) — Time in seconds (s)

Explanation: The formula calculates the instantaneous velocity based on the ratio of cylinder to pipe area, multiplied by the angular motion components and the sine function of the angular displacement over time.

3. Importance of Liquid Velocity Calculation

Details: Calculating liquid velocity is crucial for designing hydraulic systems, determining flow rates, optimizing pump performance, and ensuring proper system operation in various engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (m² for areas, rad/s for angular velocity, m for radius, s for time). All values must be positive, with time being zero or positive.

5. Frequently Asked Questions (FAQ)

Q1: What does the sine function represent in this formula?
A: The sine function represents the periodic nature of the crank motion, accounting for the changing velocity as the crank rotates through different angles.

Q2: Why is the area ratio (A/a) important?
A: The area ratio determines how much the cylinder motion is amplified or reduced when transferred to the pipe flow, affecting the resulting liquid velocity.

Q3: What are typical values for angular velocity in such systems?
A: Angular velocity values depend on the specific application but typically range from 1-10 rad/s for many mechanical systems.

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

Q5: How does crank radius affect the liquid velocity?
A: The crank radius directly scales the velocity - larger crank radius results in higher liquid velocity, assuming other parameters remain constant.