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What is a venturi - meter ? Explain its constuction and working.. |
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Answer» Solution :The ven meter isa DEVICE to measure the FLOW speed of incompressible fluid. It consists of a TUBE with a broad diameter and a small contraction at the middle as shown in figure  A manometer in the form of a U- tube is also attached to it, with one arm at the broad neck point of the tube and the other at construction which is known as throat. The manometer contains a liquid of density `rho_(m)`. At point 1, cross section area is A and velocity of liquid is `v_(1)`. At point 2, cross section area is a and velocity of liquid is `v_(2)`. According to equation of continuity , `Av_(1)=av_(2)` `thereforev_(2)=(Av_(1))/(a)`.... (1) WRITING Bernoull.s equation at point 1,2. `P_(1)+(1)/(2)rhov_(1)^(2)+rhogh,=P_(2)+(1)/(2)rhov_(2)^(2)+rhogh_(2)` but `h_(1)=h_(2)` `thereforeP_(1)-P_(2)=(1)/(2)rhov_(2)^(2)-(1)/(2)rho_(1)^(2)` `thereforeP_(1)-P_(2)=(1)/(2)rho(A^(2)v_(1)^(2))/(a^(2))-(1)/(2)rhov_(1)^(2)` `thereforeP_(1)-P_(2)=(1)/(2)rhov_(1)^(2)[((A)/(a))^(2)-1]` ... (2) Here `Agta` , `thereforev_(1)ltv_(2)` so `P_(1)gtP_(2)` The pressure difference cause liquid in arm 1 coming down and in arm 2 liquid rise . Due to height difference , the equation of pressure difference `P_(1)-P_(2)=rho_(m)gh`.....(3) Comparing equation (2) and (3), `(1)/(2)rhov_(1)^(2)[(A^(2))/(a^(2))-1]=rho_(m)gh` `therefore(1)/(2)rho_(1)^(2)[(A^(2)-a^(2))/(a^(2))]=rho_(m)gh` `thereforev_(1)^(2)=(a^(2)(2rho_(m)gh))/(rho(A^(2)-a^(2)))` `thereforev_(1)=sqrt((2rho_(m)gh)/(rho(A^(2)-a^(2))))` ...(4) where `v_(1)` is the speed of fluid at wide neck |
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