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Q.

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

2ρm+ρaghρa

b

ρm−ρaghρa

c

2ρm−ρaghρa

d

ρm+ρaghρa

answer is C.

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Detailed Solution

Bernoulli's equation between A and B givesPAρa=PBρa+v22 ⇒v2=2PA−PBρa----(1)Also equating pressures at horizontal level of EPA+ρagy+ρagh=PB+ρagy'+ρagy+ρmgh⇒ PA+ρagh=PB+ρmgh ∵ y′=0⇒PA−PB=ρm−ρagh. ⇒v2=2ρm−ρaghρa⇒v=2ρm−ρaghρa  From(1)
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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