Diameter Of Pipe Given Head Loss Over Length Of Pipe With Discharge Calculator

Formula Used:

\[ D_{pipe} = \left( \frac{128 \times \mu \times Q \times L_p}{\pi \times \gamma_f \times h_{loss}} \right)^{1/4} \]

Dynamic Viscosity (μ):

Pa·s

Discharge in Pipe (Q):

m³/s

Length of Pipe (L_p):

Specific Weight of Liquid (γ_f):

N/m³

Head Loss due to Friction (h_loss):

Diameter of Pipe (D_pipe):

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1. What is the Pipe Diameter Formula?

The formula calculates the diameter of a pipe required to maintain a specific head loss over a given length, considering fluid properties and flow rate. It's derived from the Hagen-Poiseuille equation for laminar flow in circular pipes.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ D_{pipe} = \left( \frac{128 \times \mu \times Q \times L_p}{\pi \times \gamma_f \times h_{loss}} \right)^{1/4} \]

Where:

\( D_{pipe} \) — Diameter of pipe (m)
\( \mu \) — Dynamic viscosity (Pa·s)
\( Q \) — Discharge in pipe (m³/s)
\( L_p \) — Length of pipe (m)
\( \gamma_f \) — Specific weight of liquid (N/m³)
\( h_{loss} \) — Head loss due to friction (m)

Explanation: The formula relates pipe diameter to flow characteristics, fluid properties, and energy loss due to friction.

3. Importance of Pipe Diameter Calculation

Details: Proper pipe sizing is crucial for efficient fluid transport systems. It affects flow rate, pressure drop, energy consumption, and system performance. Undersized pipes cause excessive head loss, while oversized pipes increase material costs.

4. Using the Calculator

Tips: Enter all values in SI units. Ensure viscosity, discharge, length, specific weight, and head loss are positive values. The calculator assumes laminar flow conditions.

5. Frequently Asked Questions (FAQ)

Q1: What flow regime does this formula apply to?
A: This formula is specifically derived for laminar flow conditions (Re < 2000).

Q2: How does viscosity affect pipe diameter?
A: Higher viscosity fluids require larger pipe diameters to maintain the same head loss for a given flow rate.

Q3: Can this be used for turbulent flow?
A: No, this formula is specifically for laminar flow. For turbulent flow, different equations (like Darcy-Weisbach) should be used.

Q4: What is typical head loss in piping systems?
A: Head loss typically ranges from 1-5 m per 100 m of pipe length, but varies based on application and system requirements.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for laminar flow in circular pipes, but actual results may vary due to pipe roughness, fittings, and other system components.