A 20*10 cm Venturimeter is inserted in a vertical pipe carrying oil of sp.gr. 0.8, the flow being upwards. The difference of levels between the inlet and throat section is 50 cm. The oil mercury manometer gives a reading of 30 cm of mercury. Calculate the discharge of oil. If the manometer is replaced by 2 pressure gauges (between inlet and throat), calculate the differential pressure head between inlet and throat.
Question
A 20*10 cm Venturimeter is inserted in a vertical pipe carrying oil of sp.gr. 0.8, the flow being upwards. The difference of levels between the inlet and throat section is 50 cm. The oil mercury manometer gives a reading of 30 cm of mercury. Calculate the discharge of oil. If the manometer is replaced by 2 pressure gauges (between inlet and throat), calculate the differential pressure head between inlet and throat.
Solution
To solve this problem, we need to use the Bernoulli's equation and the equation of continuity.
Step 1: Calculate the area of the inlet and throat section. The area of the inlet (A1) = πD1^2/4 = π*(20 cm)^2/4 = 314.16 cm^2 The area of the throat (A2) = πD2^2/4 = π*(10 cm)^2/4 = 78.54 cm^2
Step 2: Calculate the velocity at the throat section (V2) using the manometer reading. The pressure difference between the inlet and throat section is given by the manometer reading. We can use this to calculate the velocity at the throat section using Bernoulli's equation. P1 - P2 = 0.5ρ(V2^2 - V1^2) Assuming the velocity at the inlet (V1) is negligible, we can simplify this to: P1 - P2 = 0.5ρV2^2 Solving for V2 gives: V2 = sqrt((P1 - P2)/(0.5ρ)) Given that the manometer reading is 30 cm of mercury, the pressure difference (P1 - P2) is 30 cm of Hg * 13.6 g/cm^3 * g = 40860 dynes/cm^2 The density of the oil (ρ) is 0.8 g/cm^3 Substituting these values in gives: V2 = sqrt((40860 dynes/cm^2)/(0.50.8 g/cm^3)) = 90.14 cm/s
Step 3: Calculate the discharge (Q) of the oil. The discharge of the oil is given by the product of the velocity at the throat section and the area of the throat section. Q = V2*A2 = 90.14 cm/s * 78.54 cm^2 = 7080 cm^3/s or 7.08 L/s
Step 4: Calculate the differential pressure head between the inlet and throat. The differential pressure head (h) is given by the difference in height between the inlet and throat section. h = 50 cm
So, the discharge of the oil is 7.08 L/s and the differential pressure head between the inlet and throat is 50 cm.
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