Change In Rate Of Flow Given Torque Exerted On Fluid Calculator

Formula Used:

\[ q_{flow} = \frac{\tau}{(r_2 \cdot V_2 - r_1 \cdot V_1)} \cdot \Delta \]

Torque Exerted on Fluid (τ):

N·m

Radial Distance 2 (r₂):

Velocity at Point 2 (V₂):

m/s

Radial Distance 1 (r₁):

Velocity at Point 1 (V₁):

m/s

Delta Length (Δ):

Rate of Flow (q_flow):

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1. What is the Change in Rate of Flow Formula?

The formula calculates the rate of flow change based on torque exerted on fluid and the difference in momentum between two radial points. It's derived from impulse-momentum principles in fluid mechanics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ q_{flow} = \frac{\tau}{(r_2 \cdot V_2 - r_1 \cdot V_1)} \cdot \Delta \]

Where:

\( q_{flow} \) — Rate of Flow (m³/s)
\( \tau \) — Torque Exerted on Fluid (N·m)
\( r_2 \) — Radial Distance 2 (m)
\( V_2 \) — Velocity at Point 2 (m/s)
\( r_1 \) — Radial Distance 1 (m)
\( V_1 \) — Velocity at Point 1 (m/s)
\( \Delta \) — Delta Length (m)

Explanation: The formula relates the torque applied to a fluid to the resulting change in flow rate, considering the momentum difference between two radial positions.

3. Importance of Rate of Flow Calculation

Details: Accurate flow rate calculation is crucial for designing fluid systems, analyzing pump performance, and understanding energy transfer in hydraulic systems.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure torque > 0, radial distances > 0, velocities > 0, and delta length > 0. The denominator (r₂·V₂ - r₁·V₁) must not be zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a negative flow rate indicate?
A: A negative flow rate typically indicates flow in the opposite direction of the reference direction used in the calculation.

Q2: When is this formula applicable?
A: This formula applies to steady, incompressible flow situations where torque and momentum changes are significant factors.

Q3: What are typical units for these measurements?
A: Torque in N·m, distances in meters, velocities in m/s, and flow rate in m³/s. Consistent units are essential.

Q4: What if the denominator equals zero?
A: The formula becomes undefined when r₂·V₂ = r₁·V₁, indicating no momentum change between the two points.

Q5: How accurate is this calculation?
A: Accuracy depends on precise measurement of all input parameters and adherence to the assumptions of the formula.