Aventuri meter is to be installed in a 63 mm bore section of a piping system to measure the flow rate of water in it. from space considerations, the maximum differential head in the mercury manometer is to be 235 mm. the maximum expected flow rate is 240 litres per minute. design the throat diameter by assuming the discharge coefficient to be 0.8

Throat diameter [tex]d_2[/tex]=28.60 mm

Explanation:

Bore diameter [tex]d_1=63mm[/tex] ⇒[tex]A_1=3.09\times 10^{-3} m^2[/tex]

Manometric deflection x=235 mm

Flow rate Q=240 Lt/min⇒ Q=.004[tex]\frac{m^3}{s}[/tex]

Coefficient of discharge [tex]C_d[/tex]=0.8

We know that discharge through venturi meter

[tex]Q=C_d\dfrac{A_1A_2\sqrt{2gh}}{\sqrt{A_1^2-A_2^2}}[/tex]

[tex]h=x(\dfrac{S_m}{S_w}-1)[/tex]

[tex]S_m[/tex]=13.6 for Hg and [tex]S_w[/tex]=1 for water.

[tex]h=0.235(\dfrac{13.6}{1}-1)[/tex]

h=2.961 m

Now by putting the all value in

[tex]Q=C_d\dfrac{A_1A_2\sqrt{2gh}}{\sqrt{A_1^2-A_2^2}}[/tex]

[tex]0.004=0.8\times \dfrac{3.09\times 10^{-3} A_2\sqrt{2\times 9.81\times 2.961}}{\sqrt{(3.09\times 10^{-3})^2-A_2^2}}[/tex]

[tex]A_2=6.42\times 10^{-4} m^2[/tex]

⇒[tex]d_2[/tex]=28.60 mm

So throat diameter [tex]d_2[/tex]=28.60 mm

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