Rate Of Flow Of Liquid Into Air Vessel Given Stroke Length Calculator

Formula Used:

\[ Qr = (A \times \omega \times (L/2)) \times (\sin(\theta) - (2/\pi)) \]

Area of Cylinder (A):

m²

Angular Velocity (ω):

rad/s

Length of Stroke (L):

Angle between Crank and Flow Rate (θ):

rad

Rate of Flow (Qr):

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1. What is the Rate of Flow Formula?

The Rate of Flow formula calculates the flow rate of liquid into an air vessel based on cylinder area, angular velocity, stroke length, and the angle between crank and flow rate. This is particularly useful in hydraulic systems and pump design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Qr = (A \times \omega \times (L/2)) \times (\sin(\theta) - (2/\pi)) \]

Where:

\( Qr \) — Rate of Flow (m³/s)
\( A \) — Area of Cylinder (m²)
\( \omega \) — Angular Velocity (rad/s)
\( L \) — Length of Stroke (m)
\( \theta \) — Angle between Crank and Flow Rate (rad)
\( \pi \) — Archimedes' constant (≈ 3.1416)

Explanation: The formula accounts for the geometric relationship between the crank angle and the flow rate in hydraulic systems with reciprocating motion.

3. Importance of Rate of Flow Calculation

Details: Accurate flow rate calculation is crucial for designing hydraulic systems, optimizing pump performance, and ensuring proper fluid delivery in various engineering applications.

4. Using the Calculator

Tips: Enter area in m², angular velocity in rad/s, stroke length in m, and angle in radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of this formula?
A: This formula describes how the flow rate varies with the crank angle in reciprocating pump systems, helping engineers design more efficient hydraulic systems.

Q2: Why is the sine function used in this formula?
A: The sine function accounts for the sinusoidal variation of piston velocity with crank angle in reciprocating motion.

Q3: What are typical units for the rate of flow?
A: Rate of flow is typically measured in cubic meters per second (m³/s) or liters per second (L/s) in hydraulic applications.

Q4: How does stroke length affect the flow rate?
A: Longer stroke lengths generally result in higher flow rates, as the piston moves through a greater volume per stroke.

Q5: 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 must be considered.