Project ForgeFluid Mechanics
Bernoulli's Equation
GATE 2016
Hard
A vertical vessel has kerosene (800 kg/m³) over water (1000 kg/m³), interface between two L-tube taps 30cm apart. Kerosene rises 20cm above the upper tap; water rises 42cm above the lower tap. The distance x (cm) of the interface above the lower tap, rounded to 1 decimal place, is
10 cm(± 0.3 accepted)
Explanation
Piezometer relation: gauge pressure at lower tap=ρwater·g·42; at upper tap=ρk·g·20. Vessel-side balance: P_lower=P_upper+ρk·g(30−x)+ρw·g·x. So 1000×42=800×20+800(30−x)+1000x ⟹ 42000=40000+200x ⟹ x=10.0cm.
Source: GATE CH 2016 (2016)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.