Question

Technicians have to determine the flow rate of water in a pipe with the aid of a venturi installation and a mercury au.oaeter. The expected water welocity is about 1.5 a/s. The pipe diameter is 40 mm and the venturi throat has a diameter of 20 mm. The venturi meter has a discharge coefficient C = 0.97. Determine what level difference can be expected in the manometer.

Answer 1

Answer:

Manometric difference x=142.85 mm.

Explanation:

Given :

 Pipe diameter $d_1=40 mm$

venturi meter $d_2=20 mm$

We can know that discharge through venturi meter is given as

$Q=C_d\dfrac{A_1A_2\sqrt{2gh}}{\sqrt {A_1^2-A_2^2}}$

$A_1=1.24\times 10^{-3},A_2=3.12\times 10^{-4}$

$Q=A_1V_1$

$Q=1.24\times 10^{-3}\times 1.5=0.00186 m^3/s$

$0.00186=0.97\dfrac{1.24\times 10^{-3}\times 3.12\times 10^{-4} \sqrt{2gh}}{\sqrt {(1.24\times 10^{-3})^2-(3.12\times 10^{-4})^2}}$

h=1.8 m

We know that $h=x\left (\dfrac{\rho_{hg}}{\rho_w}-1\right )$

Where x is the manometric deflection

⇒ $1.8=x\left (\dfrac{13600}{1000}-1\right )$

So x=14.28 mm

Manometric difference x=142.85 mm.