Discharge through runner Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume Flow Rate = pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2)*Flow Velocity at Inlet
Q = pi/4*(Do^2-Db^2)*Vfi
This formula uses 1 Constants, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Volume Flow Rate - (Measured in Cubic Meter per Second) - Volume Flow Rate is the volume of fluid that passes per unit of time.
Outer Diameter of Runner - (Measured in Meter) - Outer Diameter of Runner is the diameter of the outer surface of the runner.
Diameter of Hub - (Measured in Meter) - Diameter of Hub is the diameter of the surface of the hub which is adjacent to the fluid flow.
Flow Velocity at Inlet - (Measured in Meter per Second) - Flow Velocity at Inlet is the velocity of the flow at the entrance of the turbine.
STEP 1: Convert Input(s) to Base Unit
Outer Diameter of Runner: 3.5 Meter --> 3.5 Meter No Conversion Required
Diameter of Hub: 1.75 Meter --> 1.75 Meter No Conversion Required
Flow Velocity at Inlet: 5.84 Meter per Second --> 5.84 Meter per Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Q = pi/4*(Do^2-Db^2)*Vfi --> pi/4*(3.5^2-1.75^2)*5.84
Evaluating ... ...
Q = 42.1405384570901
STEP 3: Convert Result to Output's Unit
42.1405384570901 Cubic Meter per Second --> No Conversion Required
FINAL ANSWER
42.1405384570901 42.14054 Cubic Meter per Second <-- Volume Flow Rate
(Calculation completed in 00.004 seconds)

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Kaplan Turbine Calculators

Diameter of hub given discharge
​ LaTeX ​ Go Diameter of Hub = sqrt(Outer Diameter of Runner^2-(4/pi*Volume Flow Rate/Flow Velocity at Inlet))
Outer diameter of runner
​ LaTeX ​ Go Outer Diameter of Runner = sqrt(Volume Flow Rate/Flow Velocity at Inlet*4/pi+Diameter of Hub^2)
Velocity of flow at inlet
​ LaTeX ​ Go Flow Velocity at Inlet = Volume Flow Rate/(pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2))
Discharge through runner
​ LaTeX ​ Go Volume Flow Rate = pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2)*Flow Velocity at Inlet

Discharge through runner Formula

​LaTeX ​Go
Volume Flow Rate = pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2)*Flow Velocity at Inlet
Q = pi/4*(Do^2-Db^2)*Vfi

How does Kaplan turbine operate?

The Kaplan turbine is an inward flow reaction turbine, which means that the working fluid changes pressure as it moves through the turbine and gives up its energy. Power is recovered from both the hydrostatic head and from the kinetic energy of the flowing water. The design combines features of radial and axial turbines. The inlet is a scroll-shaped tube that wraps around the turbine's wicket gate. Water is directed tangentially through the wicket gate and spirals on to a propeller shaped runner, causing it to spin. The outlet is a specially shaped draft tube that helps decelerate the water and recover kinetic energy. The turbine does not need to be at the lowest point of water flow as long as the draft tube remains full of water. A higher turbine location, however, increases the suction that is imparted on the turbine blades by the draft tube. The resulting pressure drop may lead to cavitation. Kaplan turbine efficiencies are typically over 90%, but may be lower in very low head applications.

What are the other applications of Kaplan turbine?

Kaplan turbines are widely used throughout the world for electrical power production. They cover the lowest head hydro sites and are especially suited for high flow conditions.

Inexpensive micro turbines on the Kaplan turbine model are manufactured for individual power production designed for 3 m of head which can work with as little as 0.3 m of head at a highly reduced performance provided sufficient water flow.
Large Kaplan turbines are individually designed for each site to operate at the highest possible efficiency, typically over 90%. They are very expensive to design, manufacture and install, but operate for decades.

How to Calculate Discharge through runner?

Discharge through runner calculator uses Volume Flow Rate = pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2)*Flow Velocity at Inlet to calculate the Volume Flow Rate, The Discharge through runner formula is defined as the amount of fluid passing through the runner in a given unit of time. Volume Flow Rate is denoted by Q symbol.

How to calculate Discharge through runner using this online calculator? To use this online calculator for Discharge through runner, enter Outer Diameter of Runner (Do), Diameter of Hub (Db) & Flow Velocity at Inlet (Vfi) and hit the calculate button. Here is how the Discharge through runner calculation can be explained with given input values -> 42.14054 = pi/4*(3.5^2-1.75^2)*5.84.

FAQ

What is Discharge through runner?
The Discharge through runner formula is defined as the amount of fluid passing through the runner in a given unit of time and is represented as Q = pi/4*(Do^2-Db^2)*Vfi or Volume Flow Rate = pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2)*Flow Velocity at Inlet. Outer Diameter of Runner is the diameter of the outer surface of the runner, Diameter of Hub is the diameter of the surface of the hub which is adjacent to the fluid flow & Flow Velocity at Inlet is the velocity of the flow at the entrance of the turbine.
How to calculate Discharge through runner?
The Discharge through runner formula is defined as the amount of fluid passing through the runner in a given unit of time is calculated using Volume Flow Rate = pi/4*(Outer Diameter of Runner^2-Diameter of Hub^2)*Flow Velocity at Inlet. To calculate Discharge through runner, you need Outer Diameter of Runner (Do), Diameter of Hub (Db) & Flow Velocity at Inlet (Vfi). With our tool, you need to enter the respective value for Outer Diameter of Runner, Diameter of Hub & Flow Velocity at Inlet and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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