FlyingCircus of Physics A venturi meter is used to measure the flow speed of afl
ID: 1744285 • Letter: F
Question
A venturi meter is used to measure the flow speed of afluid in a pipe. The meter is connected between two sections of thepipe (Fig. 14-55); the cross-sectional area A of theentrance and exit of the meter matches the pipe's cross-sectionalarea. Between the entrance and exit, the fluid flows from the pipewith speed V and then through a narrow ''throat'' ofcross-sectional area a with speed v. A manometerconnects the wider portion of the meter to the narrower portion.The change in the fluid's speed is accompanied by a changep in the fluid's pressure, which causes a heightdifference h of the liquid in the two arms of themanometer. (Here p means pressure in the throatminus pressure in the pipe.) Let A equal5·a. Suppose the pressure p1 atA is 3.0 atm. Compute the values of (a)the speed V at A and (b) thespeed v at a that make the pressurep2 at a equal to zero.(c) Compute the corresponding volume flow rate ifthe diameter at A is 4.5 cm.The phenomenon that occurs ata when p2 falls to nearly zero isknown as cavitation. Please assume that the fluid is water. Thewater vaporizes into small bubbles.
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This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or N·sN/m^2 or Pakg/m^3gm/s^3timesExplanation / Answer
Just the post above fixed a little.(a) from the theory we know that the equation ofcontinuity as A1 v1 = a2v2 from the given p = p1 = 1.80atm so we get v = {2 p / [((A /a)2 - 1)]} = {2 (1.01x 105 Pa*p1) / [(1000 kg /m3)((5a / a)2 - 1)]} = .......... m /s (b) again using equation of continuity weget V = (A / a) v = (5a / a)v = ......... m /s (c) the rate of flow is A v = ( / 4) (diameter given inm)2(v) =......... m3 / s
from the given p = p1 = 1.80atm so we get v = {2 p / [((A /a)2 - 1)]} = {2 (1.01x 105 Pa*p1) / [(1000 kg /m3)((5a / a)2 - 1)]} = .......... m /s (b) again using equation of continuity weget V = (A / a) v = (5a / a)v = ......... m /s (c) the rate of flow is A v = ( / 4) (diameter given inm)2(v) =......... m3 / s