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Describe the construction and working of venturimeter and obtain an equation for the volume of liquid flowing per second through a wider entry of the tube. |
Answer» Solution :  Venturimeter : This device is used to measure the rate of flow ( or say flow speed) of the incompressible fluid flowing through a pipe. It works on the principle of Bernoulli.s theorem. It consists of two wider tubes A and A. (with cross sectional area A) connected by a narrow tube B ( with cross sectional area a). A MANOMETER in the fonn of U-tube is ALSO attached between the wide and narrow tubes. The manometer contains a liquid of DENSITY `. rho_m .` Let `P_1`be the pressure of the fluid at the wider region of the tube A. Let us assume that the fluid of density .`rho` . flows .from the pipe with speed `v_1`and into the narrow region, its .speed increases to `v_2` . ACCORDING to the Bernoulli.s equation, this increase in speed is accompanied by a decrease in the fluid pressure `P_2`at the narrow region of the tube B. Therefore, the pressure DIFFERENCE between the tubes A and B is noted by measuring the height difference`(Delta P = P_1 + P_2)`between the surfaces of the manometer liquid. From the equation of continuity, we can say that `Av_1 = av_2`which means that ` v_2= A/a v_1` Using bernoulli.s equation, ` P_1 + rho (v_1^2)/(2) = P_2 + rho (v_2^2)/(2) = P_2 + rho 1/2 (A/a v_1)^&2` from the above equation , the pressure difference ` Delta P = P_1 - P_2= rho (v_1^2)/(2) (A^2 - a^2)/(a^2)` Thus , the speed of flow of liquid at the wide end of the tube A ` v_1^^2 = (2 (Delta P)a^2)/(rho(A^2 - a^2) ) rArr v_1= sqrt((2(Delta P)a^2)/(rho (A^2 - a^2) )` The volume of the liquid flowing out per second is `V = A v_1 = A sqrt( (2 (Delta P )a^2)/(p (A^2 -a^2) ) )= a A sqrt( (2(Delta P))/(p(A^2 - a^2) ))` |
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