Project ForgeConsider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m³ and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ___________ N.
- A350π²
- 750π
- C1000π
- D3000
Explanation
A=π(1)²/4=π/4 m². ṁ=ρ1AV1=1×(π/4)×100=25π kg/s. Momentum equation on the gas: (p1−p2)A + F_wall-on-gas = ṁ(V2−V1). (p1−p2)A=10000×π/4=2500π N. ṁ(V2−V1)=25π×70=1750π N. So F_wall-on-gas=1750π−2500π=−750π N (friction opposes flow). By Newton's third law, force exerted BY the gas ON the pipe = +750π N.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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