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A venturi meter is used to measure the flow speed of a fluid in a pipe . The meter is connected between two sections of the pipe (Fig) the cross-sectional area A of the entrance and exit of the meter matches the pipe's cross-sectional area a with speed v . A manometer connects the wider portion of the meter to the narrower portion . The change in the fluid's speed is accompanied by a change Deltap in the fluid 's pressure , which causes a height difference h of the liquid in the two arms of the manometer. (Here , Deltap means pressure in the throat minus pressurein the pipe). (a) By applying Bernoulli's equation and the equation of continuity to points 1 and 2 in Fig show that V = sqrt((2 a^(2) Delta p)/(rho (a^(2) - A^(2)))) where r is the density of the fluid . |
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Answer» SOLUTION :The continuity equation yields AV = av , and Bernoulli.s equation yields `DELTA p + 1//2 rho V^(2) = 1//2 rho V^(2) ` , where `Delta p = p_(1) - p_(2)` . The first equation gives v = (A/a) V . We use this to substitute for v in the second equation and OBTAIN `Delta p + 1//2 rho V^(2) = 1//2 rho (A // a)^(2) V` . We solve this equation for V , to GET `V = sqrt((2 Delta p)/(rho (A //a)^(2) - 1)) = sqrt((2a^(2) Delta p)/(rho (A^(2) - a^(2))))` |
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