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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 . |
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Answer» Solution :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))` |
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