If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as ηxρyrx, where η,ρ,r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x , y and z are given by:

Question

If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as ηxρyrx, where η,ρ,r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x , y and z are given by:

Infinity Learn · Accepted Answer

Applying dimensional method: $$vc=$$ηxρyrZ[$$M0LT$$−$$1$$]$$=$$[ML−$$1$$ T−$$1$$]x[ML−$$3$$ $$T0$$]y[$$M0LT0$$]$$2$$ Equating powers both sides $$x+y=0$$;−$$x=$$−$$1$$∴$$x=11+y=0$$∴$$y=$$−$$1-x-3$$ $$y+z=1$$−$$1$$−$$3($$−$$1)+z=1-1+3+z=1$$∴$$Z=$$−$$1$$

If dimensions of critical velocity $v_{c}$ of a liquid flowing through a tube are expressed as $[η^{x} ρ^{y} r^{x}]$ , where $η, ρ, r$ are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x , y and z are given by:

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material