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Dimensional-Analysis,-Similitude-and-Physical-Modelling

Show that resistance F to 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))` [2069-Chaitra][8]

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

Show that resistance F to 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))`

Using Buckinghams `pi` theorem, show that the velocity through a circular orifice is given by `V=root()(2gH)*phi[D/H,mu/(rhoVH)]` Where H= head causing flow D= diameter of the orifice `rho=` specific mass `mu=` coefficient of viscosity `g=` acceleration due to gravity

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))`

Dimensional Analysis

Similitude and Physical Modelling

Fluid-Mechanics