Question

Water flows around a 6-ft diameter bridge pier with a velocity of 12 ft/s. Estimate the force (per unit length) that the water exerts on the pier. Assume that the flow can be approximated as an potential fluid flow around the front half of the cylinder, but due to flow seperation, the average pressure on the rea half is constant and approximately equal to 1/2 the pressure at point A.

Answer 1

Answer: hello the diagram related to your question is missing please the third image is the missing part of the question

Fx = 977.76 Ib/ft

Explanation:

Estimate the force that water exerts on the pier

V = 12 ft/s

D( diameter ) = 6 ft

first express the force  on the first half of the cylinder  as

Fx1 =  - $-2\int\limits^\pi _\frac{\pi }{2} {Ps*cos\beta *a} \, d\beta$   ---------------- ( 1 )

where ; Fy = 0

Ps = Po + 1/2 Pv^2 ( 1 - 4 sin^2β )  ------------- ( 2 )

Input equation (2)  into equation ( 1 )         (note :  assuming Po = 0 )

attached below is the remaining part of the solution