Calculating Pressure From Flow Rate

Pressure Equation:

\[ P = \frac{8 \mu L Q}{\pi r^4} \]

Viscosity (μ):

Pa·s

Length (L):

Flow Rate (Q):

m³/s

Radius (r):

Pressure (P):

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1. What is the Pressure Calculation Formula?

The pressure calculation formula \( P = \frac{8 \mu L Q}{\pi r^4} \) is derived from the Hagen-Poiseuille equation, which describes the pressure drop in an incompressible Newtonian fluid in laminar flow through a long cylindrical pipe.

2. How Does the Calculator Work?

The calculator uses the pressure equation:

\[ P = \frac{8 \mu L Q}{\pi r^4} \]

Where:

\( P \) — Pressure (Pa)
\( \mu \) — Dynamic viscosity (Pa·s)
\( L \) — Length of the pipe (m)
\( Q \) — Volumetric flow rate (m³/s)
\( r \) — Radius of the pipe (m)

Explanation: This equation calculates the pressure difference required to maintain a given flow rate of fluid through a pipe, considering the fluid's viscosity and the pipe's dimensions.

3. Importance of Pressure Calculation

Details: Accurate pressure calculation is essential in fluid dynamics, engineering design, plumbing systems, and medical applications (such as blood flow calculations). It helps determine the energy requirements for pumping fluids through pipes and ensures system efficiency.

4. Using the Calculator

Tips: Enter viscosity in Pa·s, length in meters, flow rate in m³/s, and radius in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What types of fluids does this equation apply to?
A: This equation applies to incompressible Newtonian fluids in laminar flow through cylindrical pipes.

Q2: What is the range of validity for this formula?
A: The formula is valid for laminar flow conditions (Reynolds number < 2300) and for pipes with constant circular cross-section.

Q3: How does pipe radius affect pressure requirements?
A: Pressure requirement is inversely proportional to the fourth power of the radius, meaning small changes in radius significantly affect pressure requirements.

Q4: Can this be used for non-circular pipes?
A: No, this specific formula is only valid for circular pipes. Different formulas exist for non-circular conduits.

Q5: What are typical viscosity values for common fluids?
A: Water at 20°C has viscosity of ~0.001 Pa·s, while honey has viscosity of ~10 Pa·s, and air has viscosity of ~0.000018 Pa·s.