Diameter of hub given discharge Calculator

✖Outer Diameter of Runner is the diameter of the outer surface of the runner.ⓘ Outer Diameter of Runner [D_o]			+10% -10%
✖Volume Flow Rate is the volume of fluid that passes per unit of time.ⓘ Volume Flow Rate [Q]			+10% -10%
✖Flow Velocity at Inlet is the velocity of the flow at the entrance of the turbine.ⓘ Flow Velocity at Inlet [V_fi]			+10% -10%

✖Diameter of Hub is the diameter of the surface of the hub which is adjacent to the fluid flow.ⓘ Diameter of hub given discharge [D_b]

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Diameter of hub given discharge Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diameter of Hub = sqrt(Outer Diameter of Runner^2-(4/pi*Volume Flow Rate/Flow Velocity at Inlet))
D_b = sqrt(D_o^2-(4/pi*Q/V_fi))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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 Cubic Meter 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.

STEP 1: Convert Input(s) to Base Unit

Outer Diameter of Runner: 3.5 Meter --> 3.5 Meter No Conversion Required
Volume Flow Rate: 43.29 Cubic Meter per Second --> 43.29 Cubic Meter per Second 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

D_b = sqrt(D_o^2-(4/pi*Q/V_fi)) --> sqrt(3.5^2-(4/pi*43.29/5.84))

Evaluating ... ...

D_b = 1.67687025561926

STEP 3: Convert Result to Output's Unit

1.67687025561926 Meter --> No Conversion Required

FINAL ANSWER

1.67687025561926 ≈ 1.67687 Meter <-- Diameter of Hub

(Calculation completed in 00.004 seconds)

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Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

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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

Diameter of hub given discharge Formula

LaTeX Go

Diameter of Hub = sqrt(Outer Diameter of Runner^2-(4/pi*Volume Flow Rate/Flow Velocity at Inlet))
D_b = sqrt(D_o^2-(4/pi*Q/V_fi))

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 Diameter of hub given discharge?

Diameter of hub given discharge calculator uses Diameter of Hub = sqrt(Outer Diameter of Runner^2-(4/pi*Volume Flow Rate/Flow Velocity at Inlet)) to calculate the Diameter of Hub, The Diameter of hub given discharge formula is used to find the diameter of the surface of the hub of an axial flow turbine. Diameter of Hub is denoted by D_b symbol.

How to calculate Diameter of hub given discharge using this online calculator? To use this online calculator for Diameter of hub given discharge, enter Outer Diameter of Runner (D_o), Volume Flow Rate (Q) & Flow Velocity at Inlet (V_fi) and hit the calculate button. Here is how the Diameter of hub given discharge calculation can be explained with given input values -> 1.67687 = sqrt(3.5^2-(4/pi*43.29/5.84)).

FAQ

What is Diameter of hub given discharge?

The Diameter of hub given discharge formula is used to find the diameter of the surface of the hub of an axial flow turbine and is represented as D_b = sqrt(D_o^2-(4/pi*Q/V_fi)) or Diameter of Hub = sqrt(Outer Diameter of Runner^2-(4/pi*Volume Flow Rate/Flow Velocity at Inlet)). Outer Diameter of Runner is the diameter of the outer surface of the runner, 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.

How to calculate Diameter of hub given discharge?

The Diameter of hub given discharge formula is used to find the diameter of the surface of the hub of an axial flow turbine is calculated using Diameter of Hub = sqrt(Outer Diameter of Runner^2-(4/pi*Volume Flow Rate/Flow Velocity at Inlet)). To calculate Diameter of hub given discharge, you need Outer Diameter of Runner (D_o), Volume Flow Rate (Q) & Flow Velocity at Inlet (V_fi). With our tool, you need to enter the respective value for Outer Diameter of Runner, Volume Flow Rate & 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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