A venturi meter is used to measure the flow speed of a fluid in a pipe. The mete

Question

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 (the figure); the cross-sectional area A of the entrance and exit of the meter matches the pipe's cross-sectional area. Between the entrance and exit, the fluid flows from the pipe with speed V and then through a narrow ''throat'' of 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 ?p in the fluid's pressure, which causes a height difference h of the liquid in the two arms of the manometer. (Here ?p means pressure in the throat minus pressure in the pipe.) Let A equal 5

Explanation / Answer

(a)

   from the theory we know that the equation ofcontinuity as

   A1 v1 = a2v2

   from the given

   ?p = p1

         = 2.10 atm

   so we get

   v = ?{2 ?p / [?((A /a)2 - 1)]}

      = ?{2 (2.1*1.013 x105 Pa) / [(1000 kg / m3)((5a /a)2 - 1)]}

      = .......... m / s

(b)

   again using equation of continuity we get

   V = (A / a) v

       = (5a / a) v

       = ......... m /s

(c)

   the rate of flow is

   A v = (? / 4) (4.5 x 10-4m2) (v)

          =......... m3 / s

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