Brine of specific gravity 1.2 is flowing through a 10 cm I.D. pipeline at a maximum flow rate of 1200 liters/min. A sharp edged orifice connected to a simple U-tube mercury manometer is to be installed for the purpose of measurements. The maximum reading of the manometer is limited to 40 cm. Assuming the orifice coefficient to be 0.62, calculate the size of the orifice required.

Data:

Density of brine (ρ) = 1.2 x 1000 kg/m^{3} = 1200 kg/m^{3}

Dia of pipe (D_{a}) = 10 cm = 0.1 m

Maximum flow rate (Q) = 1200 liters/min = 1.2 m^{3}/min = 0.02 m^{3}/sec

Maximum manometer reading (h_{m}) = 40 cm = 0.4 m of Hg

Density of manometric fluid (ρ_{m}) = 13600 kg/m^{3}

Orifice coefficient (C_{o}) = 0.62

Formulae:

Velocity at the orifice

\(\displaystyle v_b = \frac{C_o}{\sqrt{1-\beta^4}}\sqrt{\frac{2(p_a-p_b)}{\rho}} \)

Where β = D_{b}/D_{a}

D_{b} = dia of orifice

D_{a} = dia of pipe

For the U-tube manometer,

P_{a} - P_{b} = (ρ_{m} - ρ)gh_{m}

Calculations:

P_{a} - P_{b} = (13600 - 1200) x 9.812 x 0.4 = 48667.5 N/m^{2
}

The quantity (1 - β^{4}) will be approximately 1.

Therefore,

v_{b} = 0.62 x ( 2 x 48667.5 / 1200 )^{0.5} = 5.584 m/sec

Cross sectional area of orifice = volumetric flow rate / velocity at the orifice = 0.02 / 5.584 = 0.00358 m^{2}

Dia of orifice (D_{b}) = (0.00358 x 4/π)^{0.5} = 0.0675 m = **6.75 cm**

Last Modified on: 01-May-2024

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