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The torque developed by a water turbine depends on discharge Q head H, specific weight `gamma`, angular velocity `omega` and efficiency `eta`. Prove that using suitable dimensional analysis , equation will be: `T=rhogH^4*f(Q/(omegaH^3),eta)` [2066-Bhadra][8]

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This Chapter Dimensional-Analysis,-Similitude-and-Physical-Modelling consists of the following topics

The viscosity of gas depends on its density, mean velocity of molecules, diameter of molecules, and mean path length. Applying Buckingham's theorem, develop the expression for viscosity.

The torque developed by a water turbine depends on discharge Q head H, specific weight `gamma`, angular velocity `omega` and efficiency `eta`. Prove that using suitable dimensional analysis , equation will be: `T=rhogH^4*f(Q/(omegaH^3),eta)`

Show that the resistance F to the motion of a sphere of diameter D moving with uniform velocity `V` through a real fluid of density `rho` and viscosity `mu` is given by, `F=rhoD^2V^2*f(mu/(rhoVD))`

The torque developed by a water turbine depends on discharge Q head H

specific weight `gamma`

angular velocity `omega` and efficiency `eta`. Prove that using suitable dimensional analysis

the equation will be: `T=rhogH^4*f(Q/(omegaH^3)

eta)`

Dimensional Analysis

Similitude and Physical Modelling

Fluid-Mechanics