A venturimeter having area of 700 cm² × 150 cm² is inserted in a vertical pipe carrying water, flowing in the upward direction. A differential manometer connected to the inlet and throat gives a reading of 20 cm. What is the approximate discharge by assuming Cd = 1·0 and g = 1000 cm/s² ?
- A110 L/sCorrect
- B100 L/s
- C125 L/s
- D95 L/s
Solution
Concept
Discharge through a venturimeter with a mercury manometer
Formula
Q = Cd A₁A₂ √(2gh) / √(A₁² − A₂²), h = x (Sm/S − 1)
Step-by-step solution
1. h = 20 × (13.6 − 1) = 252 cm of water (mercury manometer). 2. A₁A₂/√(A₁² − A₂²) = 700 × 150 / √(700² − 150²) = 105 000 / 683.7 = 153.6 cm². 3. √(2gh) = √(2 × 1000 × 252) = 710 cm/s. 4. Q = 153.6 × 710 = 1.09 × 10⁵ cm³/s ≈ 109 L/s ≈ 110 L/s.
Explanation
The inclination of the pipe does not affect the discharge because the differential manometer measures the piezometric head difference directly. The mercury reading is converted to a head of water by the factor 12.6.
Why the other options are wrong
100, 95 and 125 L/s do not match 109 L/s. Using the water-equivalent head of 20 cm instead of 252 cm would give only about 31 L/s.
Shortcut
h = 12.6 x for a mercury manometer.
Common mistake
Using the manometer reading directly as the head.
Correct answer: A) 110 L/s