Figure shows a device called Pitot tube . It measures the velocity of moving fluids . Determine the velocity of the fluid in terms of the density `rho` the density of the fluid in manometer (U-tube) `sigma` and the height h .

Explanation

The fluid inside the right tube must be at rest as the fluid exactly at the end is in contact with the fluid in Pitot tube , which is at rest .
The velocity `v_(1)` is the fluid velocity `v_(f)` . The velocity `v_(2)` of the fluid at point B is zero and the pressure in the right arm is `p_(2)` (called stagnation pressure ) .
Thus , using Bernoulli.s principle
`rho_(1) + (1)/(2) rho v_(1)^(2) = p_(2) + (1)/(2) rho v_(2)`
we get `rho_(2) = p_(1) + (1)/(2) rho v_(f)^(2)`
On the other hand , the openings at point A is not along the flow lines , so we do not need to use Bernoulli.s equation . We can simply say that the pressure just outside the opening is same as that within the Pitot tube .
Therefore , the pressure at the left arm of the manometer is same as the fluid pressure `p_(f)` , that is `p_(1) = p_(f)` .
Also `p_(2) = p_(1) + (rho - sigma) gh " " (14-54)`
Generally , `sigma lt lt rho` , so it is ignored .
Thus , `p_(2) = p_(f) + rho gh " " (14-55)`
From Eqs. 14-54 and 14-55
`(1)/(2) sigma v_(f)^(2) = rho g h `
or ` v_(f) = sqrt((2 rho gh )/(sigma))`