Rate Of Flow Given Pressure Gradient Calculator

Formula Used:

\[ Q = 0.5 \times V_{mean} \times h - \frac{\frac{dp}{dr} \times h^3}{12 \times \mu} \]

Mean Velocity (V_mean):

m/s

Height of Channel (h):

Pressure Gradient (dp/dr):

N/m³

Dynamic Viscosity (μ):

Pa·s

Discharge in Pipe (Q):

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1. What is the Rate of Flow Given Pressure Gradient?

The Rate of Flow Given Pressure Gradient formula calculates the discharge in a pipe or channel based on mean velocity, channel height, pressure gradient, and dynamic viscosity. This equation is particularly useful in fluid mechanics for analyzing flow characteristics in various engineering applications.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ Q = 0.5 \times V_{mean} \times h - \frac{\frac{dp}{dr} \times h^3}{12 \times \mu} \]

Where:

\( Q \) — Discharge in pipe (m³/s)
\( V_{mean} \) — Mean velocity (m/s)
\( h \) — Height of channel (m)
\( \frac{dp}{dr} \) — Pressure gradient (N/m³)
\( \mu \) — Dynamic viscosity (Pa·s)

Explanation: This equation accounts for both the convective flow component (first term) and the pressure-driven flow component (second term) to determine the total discharge in the system.

3. Importance of Flow Rate Calculation

Details: Accurate flow rate calculation is essential for designing piping systems, optimizing fluid transport, ensuring proper system operation, and maintaining efficiency in various industrial and engineering applications.

4. Using the Calculator

Tips: Enter mean velocity in m/s, channel height in meters, pressure gradient in N/m³, and dynamic viscosity in Pa·s. All values must be valid (height and viscosity > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the pressure gradient in this formula?
A: The pressure gradient represents the rate of pressure change along the flow direction, which drives the fluid motion and significantly affects the overall discharge rate.

Q2: How does dynamic viscosity influence the flow rate?
A: Higher dynamic viscosity increases resistance to flow, reducing the discharge rate for a given pressure gradient and channel geometry.

Q3: When is this formula most applicable?
A: This formula is particularly useful for analyzing flow in rectangular channels or between parallel plates where the height dimension is significant.

Q4: What are the limitations of this equation?
A: The equation assumes steady, laminar flow and may not be accurate for turbulent flow conditions or complex geometries.

Q5: How does channel height affect the flow rate?
A: Flow rate increases with channel height, but the relationship is non-linear due to the cubic term in the pressure-driven component of the equation.