Project ForgeFluid Mechanics
Bernoulli's Equation
GATE 2009
Hard
For the same free jet system (nozzle velocity ≈27.1 m/s, nozzle diameter 75mm, pipe diameter 225mm, nozzle tip 0.5m above point B in the pipe), the gauge pressure (in kPa) at point B is
- A80.0
- B100.0
- C239.3
- 367.6
Explanation
By continuity, VB=Vnozzle×(Dnozzle/Dpipe)²=27.13×(75/225)²=27.13/9≈3.01 m/s. Bernoulli from B to the nozzle exit (atmospheric, elevated by 0.5m): PB(gauge)=ρ[(Vnozzle²−VB²)/2+g(0.5)]=1000×[(735.8−9.08)/2+4.905]≈368,000 Pa≈367.6 kPa.
Source: GATE CH 2009 (2009)
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