Radial Distance r1 Given Torque Exerted on Fluid Calculator

Formula Used:

\[ r1 = \frac{(r2 \times V2 \times qflow) - (\tau \times \Delta)}{qflow \times V1} \]

Radial Distance 2 (r2):

Velocity at Point 2 (V2):

m/s

Rate of Flow (qflow):

m³/s

Torque Exerted on Fluid (τ):

N·m

Delta Length (Δ):

Velocity at Point 1 (V1):

m/s

Radial Distance 1 (r1):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Radial Distance r1 Given Torque Exerted on Fluid?

This calculator determines the initial radial distance (r1) in fluid mechanics using the impulse-momentum principle. It calculates the distance from a reference point based on torque exerted on fluid, flow rate, and velocities at two points.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r1 = \frac{(r2 \times V2 \times qflow) - (\tau \times \Delta)}{qflow \times V1} \]

Where:

\( r1 \) — Radial distance 1 (m)
\( r2 \) — Radial distance 2 (m)
\( V2 \) — Velocity at point 2 (m/s)
\( qflow \) — Rate of flow (m³/s)
\( \tau \) — Torque exerted on fluid (N·m)
\( \Delta \) — Delta length (m)
\( V1 \) — Velocity at point 1 (m/s)

Explanation: The formula applies the impulse-momentum principle to calculate the initial radial distance based on the balance between momentum changes and applied torque in a fluid system.

3. Importance of Radial Distance Calculation

Details: Accurate calculation of radial distances is crucial for analyzing fluid dynamics in rotating systems, designing turbomachinery, and understanding momentum transfer in fluid mechanics applications.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure all inputs are positive values (except torque and delta length which can be zero). The calculator will compute radial distance 1 based on the provided parameters.

5. Frequently Asked Questions (FAQ)

Q1: What is the impulse-momentum principle?
A: The impulse-momentum principle states that the impulse of a force acting on a system equals the change in momentum of that system.

Q2: When is this calculation particularly useful?
A: This calculation is essential in analyzing centrifugal pumps, turbines, and other rotating fluid machinery where torque and momentum transfer are significant factors.

Q3: What are typical units for these measurements?
A: Radial distances in meters (m), velocities in meters per second (m/s), flow rate in cubic meters per second (m³/s), and torque in Newton-meters (N·m).

Q4: Can this formula be applied to compressible fluids?
A: The formula is primarily designed for incompressible flow assumptions. For compressible fluids, additional factors like density changes must be considered.

Q5: What if the denominator becomes zero?
A: If either flow rate or velocity at point 1 is zero, the calculation becomes undefined as division by zero is mathematically impossible.