Can someone help me work this physics question out?? Please? A Pitot tube, is a

Question

Can someone help me work this physics question out?? Please?

A Pitot tube, is a fluid-speed measuring device that has applications in many fields, including physiology. Often used on airplanes to measure the airspeed of the craft, it can be seen mounted on the wings or fuselage.

At the front opening, the steamlines part and there is a stagnation point there. The fluid rushes away from that point in all directions, and its speed there is zero. Accordingly, the pressure (P) there and all along the inner tube is relatively high. On the other hand, the speed of the fluid over any of the small holes in the outer cylinder is the undisturbed

freestream speed (v). Derive an expression for v in terms of the pressure difference indicated by the attached manometer, keeping in mind that the air within the device is at rest. BTW, the device was first used by Henri Pitot to measure water speeds in the Seine River (1730).

Can someone help me work this physics question out?? Please? A Pitot tube, is a fluid-speed measuring device that has applications in many fields, including physiology. Often used on airplanes to measure the airspeed of the craft, it can be seen mounted on the wings or fuselage. At the front opening, the steamlines part and there is a stagnation point there. The fluid rushes away from that point in all directions, and its speed there is zero. Accordingly, the pressure (P) there and all along the inner tube is relatively high. On the other hand, the speed of the fluid over any of the small holes in the outer cylinder is the undisturbed freestream speed (v). Derive an expression for v in terms of the pressure difference indicated by the attached manometer, keeping in mind that the air within the device is at rest. BTW, the device was first used by Henri Pitot to measure water speeds in the Seine River (1730).

Explanation / Answer

according to Bernoulli's teorem

p+1/2 rho v^2 = constant (if difference in height is not there and the flow can be assumed to be incompressible and irrotational)

rho = density of fluid

p0 = stagnation pressure

p = outside region pressure

p+1/2 rho v^2 = p0

v = sqrt(2(p0-p)/rho)

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