Exercise -1

A pitot tube is installed at the centre of a pipe of diameter 0.3m. The pipe carries air at   Air is flowing at  gauge pressure. Pitot tube measures a pressure difference of 50 mm water. Calculate flow rate of air in pipe. Assume pitot coefficient unity.

SOLUTION

Equation 9 of lecture 22 states that
 

Note that the pitot tube is installed at the centre of the pipe. At the centre one would measure maximum velocity of gas. and hence   would also be maximum. Hence  . Inserting   and  in appropriate units.

 
, when maximum velocity is used.
However, there is a radial velocity distribution. The velocity of the fluid will be maximum at the centre and minimum at the pipe surface. There would be a parabolic profile. Flow rate must be calculated by using average velocity. For the turbulent flow we use equation 11 of the lecture 22