A Pitot tube is shown in figure. Wind blows in the direction shown. Air at inlet A is brought to rest, whereas its speed just outside of opening B is unchanged. The U tube contains mercury of density ρm. Find the speed of wind with respect to Pitot tube. Neglect the height difference between A and B and take the density of air as ρa.
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a
2(ρm+ρa)ghρa
b
2(ρm-ρa)ghρa
c
(ρm-ρa)ghρa
d
(ρm+ρa)ghρa
answer is B.
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Detailed Solution
Bernoulli's equation between A and B givespAρa = pBρa+v22 ⇒ v2 = 2[pA-pBρa]Also equating pressures at horizontal level of EpA+ρagy+ρagh = pB+ρagy'+ρagy+ρmgh [∵ y' = 0]pA+ρagh = pB+ρmghpA-pB = (ρm-ρa)ghv2 = 2(ρm-ρa)ghρav = 2(ρm-ρa)ghρa