Project ForgeFluid Mechanics
Bernoulli's Equation
GATE 2013
Medium
Water (density 1000 kg/m³) is flowing through a nozzle and exiting to the atmosphere. D1=4D2. The average velocity of the stream at location 2 is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa. Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1 is _____
137500 Pa(± 2000 accepted)
Explanation
By continuity, A1V1=A2V2. Since D1=4D2, A1=16A2, so V1=V2/16=16/16=1 m/s. Bernoulli with friction: P1+½ρV1²=P2+½ρV2²+ΔPfriction. P2=0 (gauge, exiting to atmosphere). P1=½ρ(V2²−V1²)+ΔPfriction=½×1000×(256−1)+10000=127,500+10,000=137,500 Pa.
Source: GATE CH 2013 (2013)
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