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

The force in a circular cylinder depends on free stream velocity V, diameter of cylinder D, density of fluid `rho`, viscosity of fluid `mu`, and time t. By using Buckinghamâ??s `pi` orem show that `F=rhoV^2D^2*phi(mu/(rhoVD),(Vt)/D)` Take `rho,V, D` as repeating variables. [2070-Ashad][8]

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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

The force in a circular cylinder depends on free stream velocity V, diameter of cylinder D, density of fluid `rho`, viscosity of fluid `mu`, and time t. By using Buckinghamâ??s `pi` orem show that `F=rhoV^2D^2*phi(mu/(rhoVD),(Vt)/D)` Take `rho,V, D` as repeating variables.

Given:Draining of tank from initial level `h_0` , time `T`, depends on tank diameter `D`, orifice diameter `d`,acceleration due to gravity `g`, density `rho` and viscosity ``mu`. find:
  • Number of dimensionless parameters
  • Number of repeating variables
  • `pi-` parameters containing viscosity.

The force in a circular cylinder depends on the free stream velocity V

diameter of cylinder D

density of fluid `rho`

viscosity of fluid `mu`

and time t. By using Buckinghamâ??s `pi` theorem show that `F=rhoV^2D^2*phi(mu/(rhoVD)

(Vt)/D)` Take `rho

V

D` as repeating variables.

Dimensional Analysis

Similitude and Physical Modelling

Fluid-Mechanics