## Outer diameter of runner Solution

STEP 0: Pre-Calculation Summary
Formula Used
Outer diameter of runner = sqrt((Volume Flow Rate/Flow velocity at inlet)*(4/pi)+(Diameter of hub^2))
Do = sqrt((Q/Vf1)*(4/pi)+(Db^2))
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Outer diameter of runner - (Measured in Meter) - Outer diameter of runner is the diameter of the outer surface of the runner.
Volume Flow Rate - (Measured in Meter³ per Second) - Volume Flow Rate is the volume of fluid that passes per unit of time.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Volume Flow Rate: 1.5 Meter³ per Second --> 1.5 Meter³ per Second No Conversion Required
Flow velocity at inlet: 10 Meter per Second --> 10 Meter per Second No Conversion Required
Diameter of hub: 1.75 Meter --> 1.75 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Do = sqrt((Q/Vf1)*(4/pi)+(Db^2)) --> sqrt((1.5/10)*(4/pi)+(1.75^2))
Evaluating ... ...
Do = 1.80374220212043
STEP 3: Convert Result to Output's Unit
1.80374220212043 Meter --> No Conversion Required
1.80374220212043 Meter <-- Outer diameter of runner
(Calculation completed in 00.031 seconds)
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## < 7 Kaplan Turbine Calculators

Diameter of hub given discharge
Diameter of hub = sqrt((Outer diameter of runner^2)-((4/pi)*(Volume Flow Rate/Flow velocity at inlet))) Go
Outer diameter of runner
Outer diameter of runner = sqrt((Volume Flow Rate/Flow velocity at inlet)*(4/pi)+(Diameter of hub^2)) Go
Vane angle at inlet and outlet at extreme edge of runner
Vane angle at inlet = atan((Flow velocity at inlet)/(Whirl velocity at inlet-Velocity of the vane at the inlet)) Go
Velocity of flow at inlet
Flow velocity at inlet = Volume Flow Rate/((pi/4)*((Outer diameter of runner^2)-(Diameter of hub^2))) Go
Discharge through runner
Volume Flow Rate = (pi/4)*((Outer diameter of runner^2)-(Diameter of hub^2))*Flow velocity at inlet Go
Flow velocity given whirl velocity
Flow velocity at inlet = Whirl velocity at inlet*tan(Guide blade angle) Go
Whirl velocity at inlet
Whirl velocity at inlet = Flow velocity at inlet/tan(Guide blade angle) Go

## Outer diameter of runner Formula

Outer diameter of runner = sqrt((Volume Flow Rate/Flow velocity at inlet)*(4/pi)+(Diameter of hub^2))
Do = sqrt((Q/Vf1)*(4/pi)+(Db^2))

## 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 Outer diameter of runner?

Outer diameter of runner calculator uses Outer diameter of runner = sqrt((Volume Flow Rate/Flow velocity at inlet)*(4/pi)+(Diameter of hub^2)) to calculate the Outer diameter of runner, The Outer diameter of runner formula is used to obtain the outer diameter of the runner which is the outermost surface adjacent to the fluid flow. Outer diameter of runner is denoted by Do symbol.

How to calculate Outer diameter of runner using this online calculator? To use this online calculator for Outer diameter of runner, enter Volume Flow Rate (Q), Flow velocity at inlet (Vf1) & Diameter of hub (Db) and hit the calculate button. Here is how the Outer diameter of runner calculation can be explained with given input values -> 1.803742 = sqrt((1.5/10)*(4/pi)+(1.75^2)).

### FAQ

What is Outer diameter of runner?
The Outer diameter of runner formula is used to obtain the outer diameter of the runner which is the outermost surface adjacent to the fluid flow and is represented as Do = sqrt((Q/Vf1)*(4/pi)+(Db^2)) or Outer diameter of runner = sqrt((Volume Flow Rate/Flow velocity at inlet)*(4/pi)+(Diameter of hub^2)). Volume Flow Rate is the volume of fluid that passes per unit of time, Flow velocity at inlet is the velocity of the flow at the entrance of the turbine & Diameter of hub is the diameter of the surface of the hub which is adjacent to the fluid flow.
How to calculate Outer diameter of runner?
The Outer diameter of runner formula is used to obtain the outer diameter of the runner which is the outermost surface adjacent to the fluid flow is calculated using Outer diameter of runner = sqrt((Volume Flow Rate/Flow velocity at inlet)*(4/pi)+(Diameter of hub^2)). To calculate Outer diameter of runner, you need Volume Flow Rate (Q), Flow velocity at inlet (Vf1) & Diameter of hub (Db). With our tool, you need to enter the respective value for Volume Flow Rate, Flow velocity at inlet & Diameter of hub 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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