Pressure Head When Connecting Rod Is Not Very Long As Compared To Crank Length Calculator

Formula Used:

\[ h_a = \frac{L_1 \cdot A \cdot \omega^2 \cdot r \cdot \cos(\theta)}{[g] \cdot a} \cdot \left( \cos(\theta) + \frac{\cos(2\theta)}{n} \right) \]

Length of Pipe 1 (L₁):

Area of Cylinder (A):

m²

Angular Velocity (ω):

rad/s

Radius of Crank (r):

Angle Turned by Crank (θ):

rad

Area of Pipe (a):

m²

Ratio of Length of Connecting Rod to Crank Length (n):

Pressure Head due to Acceleration (hₐ):

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1. What is Pressure Head due to Acceleration?

Pressure Head due to Acceleration of liquid is defined as the ratio of the intensity of pressure to the weight density of the liquid. This formula specifically applies when the connecting rod is not very long as compared to the crank length in reciprocating pump systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ h_a = \frac{L_1 \cdot A \cdot \omega^2 \cdot r \cdot \cos(\theta)}{[g] \cdot a} \cdot \left( \cos(\theta) + \frac{\cos(2\theta)}{n} \right) \]

Where:

\( h_a \) — Pressure Head due to Acceleration (m)
\( L_1 \) — Length of Pipe 1 (m)
\( A \) — Area of cylinder (m²)
\( \omega \) — Angular Velocity (rad/s)
\( r \) — Radius of crank (m)
\( \theta \) — Angle turned by crank (rad)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( a \) — Area of pipe (m²)
\( n \) — Ratio of length of connecting rod to crank length

Explanation: This formula accounts for the acceleration effects in reciprocating pump systems where the connecting rod length is not significantly longer than the crank length.

3. Importance of Pressure Head Calculation

Details: Accurate pressure head calculation is crucial for designing and analyzing reciprocating pump systems, ensuring proper fluid flow characteristics, and preventing cavitation or other flow-related issues.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive and within reasonable physical limits for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: When is this formula applicable?
A: This formula is specifically designed for cases where the connecting rod is not very long compared to the crank length in reciprocating pump systems.

Q2: What are typical values for the ratio n?
A: The ratio n (connecting rod length to crank length) typically ranges from 3 to 6 in most reciprocating pump designs.

Q3: How does angular velocity affect the pressure head?
A: Pressure head increases with the square of angular velocity, making it a significant factor in the calculation.

Q4: What is the significance of the cosine terms?
A: The cosine terms account for the varying mechanical advantage and acceleration components as the crank rotates through different angles.

Q5: Are there limitations to this equation?
A: This equation assumes ideal fluid behavior and may need adjustments for highly viscous fluids or systems with significant friction losses.