Project ForgeFluid Mechanics
Bernoulli's Equation & Flow
GATE 2008
Hard
For the same descending circular plate (squeeze-film flow, vr=Vr/2h with h decreasing at rate V), the radial component of the fluid acceleration at r=R is
- 3V²R/4h²
- BV²R/4h²
- CV²R/2h²
- DV²h/4R²
Explanation
vr=Vr/(2h(t)) with dh/dt=-V. ∂vr/∂t=(Vr/2)(-1/h²)(dh/dt)=(Vr/2)(V/h²)=V²r/(2h²). Convective term vr·∂vr/∂r=[Vr/(2h)][V/(2h)]=V²r/(4h²). Total ar=V²r/(2h²)+V²r/(4h²)=3V²r/(4h²); at r=R, ar=3V²R/(4h²).
Source: GATE ME 2008 (2008)
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.