Work Done Per Second On Runner By Water For Acute Angled Outlet Blade Calculator

Formula Used:

\[ W = \rho_f \times Q_f \times (V_{w1} \times u_1 + V_{w2} \times u_2) \]

Density of Fluid (ρf):

kg/m³

Volume Flow Rate (Qf):

m³/s

Whirl Velocity at Inlet (Vw1):

m/s

Velocity of Vane at Inlet (u1):

m/s

Whirl Velocity at Outlet (Vw2):

m/s

Velocity of Vane at Outlet (u2):

m/s

Work Done Per Second (W):

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1. What is Work Done Per Second On Runner By Water For Acute Angled Outlet Blade?

The Work Done Per Second On Runner By Water For Acute Angled Outlet Blade is defined as the amount of work that is done by the Francis turbine in a given unit of time. It represents the power output of the turbine system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ W = \rho_f \times Q_f \times (V_{w1} \times u_1 + V_{w2} \times u_2) \]

Where:

\( W \) — Work Done Per Second (Watt)
\( \rho_f \) — Density of Fluid (kg/m³)
\( Q_f \) — Volume Flow Rate (m³/s)
\( V_{w1} \) — Whirl Velocity at Inlet (m/s)
\( u_1 \) — Velocity of Vane at Inlet (m/s)
\( V_{w2} \) — Whirl Velocity at Outlet (m/s)
\( u_2 \) — Velocity of Vane at Outlet (m/s)

Explanation: The formula calculates the work done per second by considering the fluid density, flow rate, and the product of whirl velocities and vane velocities at both inlet and outlet.

3. Importance of Work Done Calculation

Details: Accurate calculation of work done per second is crucial for evaluating turbine efficiency, power output assessment, and system performance optimization in hydraulic turbine applications.

4. Using the Calculator

Tips: Enter all required parameters in their respective units. Ensure density and flow rate are positive values, and all velocity measurements are accurate for reliable results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of whirl velocity in this calculation?
A: Whirl velocity represents the tangential component of absolute velocity, which directly contributes to the torque and work done by the turbine.

Q2: How does fluid density affect the work done?
A: Higher fluid density increases the mass flow rate, resulting in greater work done per second for the same velocity conditions.

Q3: What are typical values for these parameters in real turbines?
A: Values vary significantly based on turbine design, but typical densities range 800-1000 kg/m³, flow rates 1-100 m³/s, and velocities 5-50 m/s.

Q4: Why are both inlet and outlet velocities considered?
A: Both contribute to the overall energy transfer. The difference between inlet and outlet conditions determines the net work extracted.

Q5: Can this formula be used for other turbine types?
A: While similar principles apply, specific formulas may vary for different turbine designs (Pelton, Kaplan, etc.).