An oil of specific gravity 0.8 is flowing a venturi meter having inlet diameter 20 cm and throat diameter of 10 cm. The oil differential manometer shows a reading of 25 cm. Calculate the difference of pressure head. Specific gravity of mercury is 13.6.

Concept:

For venturimeter,

\({\rm{Pressure\;head\;difference\;}}\left( h \right) = x \times \left( {\frac{{{S_m}}}{{{S_0}}} - 1} \right)\)

Where x = reading, S_m = liquid with higher specific gravity, S_o = liquid with lower specific gravity.

Calculation:

Given:

S_o = 0.8, x = 0.25 m = 0.2 m, D₁ = 0.2 m, D₂ = 0.1 m, S_m = 13.6

Now,

\({\rm{Pressure\;head\;difference\;}}\left( h \right) = x \times \left( {\frac{{{S_m}}}{{{S_0}}} - 1} \right)\)

\(h = 0.25\left( {\frac{{13.6}}{{0.8}} - 1} \right)\)

∴ h = 4 m = 400 cm

Important Points

The rate of flow through the Venturimeter is given as:

\({\rm{Rate\;of\;flow\;}}\left( Q \right) = \frac{{{C_d} \cdot {A_1}{A_2}\sqrt {2gh} }}{{\sqrt {A_1^2 - A_2^2} }}\)

Where Cd = Coefficient of discharge; A1 = Area at throat; A2 = Area at inlet; h = Pressure head difference;