Velocity At Radial Distance R2 Given Torque Exerted On Fluid Calculator

Formula Used:

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

Rate of Flow (q_flow):

m³/s

Radial Distance 1 (r₁):

Velocity at Point 1 (V₁):

m/s

Torque Exerted on Fluid (τ):

N·m

Delta Length (Δ):

Radial Distance 2 (r₂):

Velocity at Point 2 (V₂):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Velocity at Radial Distance r2?

Velocity at Radial Distance r2 represents the velocity of fluid at a specific radial distance from the reference point in a flow system, considering the torque exerted on the fluid and other flow parameters.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the velocity at a different radial position by considering the momentum balance and torque effects in the fluid flow system.

3. Importance of Velocity Calculation

Details: Accurate velocity calculation is crucial for analyzing fluid dynamics, designing flow systems, predicting flow behavior, and optimizing energy transfer in various engineering applications.

4. Using the Calculator

Tips: Enter all parameters in appropriate SI units. Ensure all values are positive and non-zero (except velocity and torque which can be zero). Rate of flow and radial distances must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What happens if the rate of flow is zero?
A: The formula becomes undefined as it involves division by zero. The calculator will display "Undefined (Division by Zero)" in such cases.

Q2: Can this formula be used for compressible fluids?
A: This specific formulation is typically used for incompressible fluid flow analysis. For compressible fluids, additional factors need to be considered.

Q3: What is the physical significance of torque in fluid flow?
A: Torque represents the rotational force effect on the fluid, which can be caused by external forces, impellers, or other rotating elements in the flow system.

Q4: How does radial distance affect velocity calculation?
A: Radial distance affects the moment arm in the momentum balance equation, influencing how torque and flow rate contribute to the velocity at different positions.

Q5: What are typical applications of this calculation?
A: This calculation is commonly used in turbomachinery design, pipe flow analysis, hydraulic systems, and any application involving rotational fluid dynamics.