Diameter of Pipe given Pressure Drop over Length of Pipe with Discharge Calculator

Formula Used:

\[ D_{pipe} = \left( \frac{128 \cdot \mu \cdot Q \cdot L_p}{\Delta P \cdot \pi} \right)^{1/4} \]

Dynamic Viscosity (μ):

Pa·s

Discharge in Pipe (Q):

m³/s

Length of Pipe (Lₚ):

Pressure Difference (ΔP):

Diameter of Pipe (Dₚᵢₚₑ):

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1. What is the Pipe Diameter Formula?

The formula calculates the diameter of a pipe required to maintain a specific pressure drop over a given length for a fluid with known viscosity 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:

\[ D_{pipe} = \left( \frac{128 \cdot \mu \cdot Q \cdot L_p}{\Delta P \cdot \pi} \right)^{1/4} \]

Where:

\( D_{pipe} \) — Diameter of pipe (m)
\( \mu \) — Dynamic viscosity (Pa·s)
\( Q \) — Discharge in pipe (m³/s)
\( L_p \) — Length of pipe (m)
\( \Delta P \) — Pressure difference (Pa)
\( \pi \) — Mathematical constant pi (≈3.1416)

Explanation: The formula calculates the fourth root of the ratio between the viscous resistance term (128μQLₚ) and the pressure driving force (ΔPπ).

3. Importance of Pipe Diameter Calculation

Details: Accurate pipe diameter calculation is crucial for designing efficient fluid transport systems, ensuring adequate flow rates while minimizing pressure losses and energy consumption in piping networks.

4. Using the Calculator

Tips: Enter dynamic viscosity in Pa·s, discharge in m³/s, pipe length in meters, and pressure difference in Pascals. All values must be positive and non-zero for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What flow regime does this formula apply to?
A: This formula is specifically for laminar flow conditions (Re < 2300) where the flow is smooth and orderly.

Q2: Can this formula be used for turbulent flow?
A: No, for turbulent flow, different equations (like Darcy-Weisbach or Hazen-Williams) must be used as the relationship between flow parameters changes significantly.

Q3: What are typical viscosity values for common fluids?
A: Water at 20°C: ~0.001 Pa·s, Air at 20°C: ~0.000018 Pa·s, Engine oil: ~0.1-0.3 Pa·s, Honey: ~2-10 Pa·s.

Q4: How does pipe diameter affect pressure drop?
A: Pressure drop is inversely proportional to the fourth power of diameter - doubling the diameter reduces pressure drop by a factor of 16 for the same flow rate.

Q5: What are practical limitations of this calculation?
A: Assumes Newtonian fluid, constant viscosity, smooth pipe walls, fully developed flow, and neglects entrance effects and minor losses.