Please use Bernouille\'s Equation with these terms: P 1 +0.5 ?v 1 ^2 + ?gh 1 = P

Question

Please use Bernouille's Equation with these terms:

P1 +0.5?v1^2 + ?gh1 = P2+0.5?v2^2 + ?gh2

And also this equation:

A1v1 = A2v2

Where P1  represents the pressure 1 and pressure 2, and so forth.

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Step by step would really be appreciated!!

Air is blown through a circular and horizontal Venturi tube, as shown in the figure below. The diameters of the narrow and wider sections of the tube are given, and the height h of the mercury column is measured to be 7.21 mm. What are the air speeds in the wider and the narrower sections of the tube? The density of mercury is 13,600 kg/m3. (Assume the density of air is 1.29 kg/m3.) v1=m/s v2=m/s

Explanation / Answer

USING CONTINUITY EQUATION,

A1v1=A2v2, where A1=pi*(d1/2)^2 & A2=pi*(d2/2)^2,d1=3cm;d2=1 cm

So, v1/v2=A2/A1=(d2/d1)^2=1/9. (1)

Using bernoulli theorm between points 1 & 2,we have

P1 +0.5?v1^2 + ?gh1 = P2+0.5?v2^2 + ?gh2 (S0 h1=h2).

0.5?(v2^2-v1^2)=P1-P2

& P1-P2=?(mercury)*gh

hence,0.5?(v2^2-v1^2)=?(mercury)*gh (2)

using euation 1, putting value of v2 in tems of v1 in equation 2,we have

0.5?(9v1^2-v1^2)=?(mercury)*gh

Solving this,we have

v1=13.65m/s

v2=9v1=122.82m/s

So in wider tube velocity=13.65m/s

& in narrower tube velocity=122.82m/s

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