fluids motion HARD!. i attached the file as a PDF check picture from Q4

gikwiye

1. The problem statement, all variables and given/known dataµ

Q.4 An incompressible fluid of density ρ flows steadily through a two-dimensional infinite row of fixed vanes,
a few of which are shown below. The vane spacing is a. The velocities V1 and V2 and pressures p1 and p2
are all constant along their respective stations, (1) and (2). The directions of the two velocities are given by
the angles β1 and β2, as shown. Find the horizontal and vertical components of the force necessary to keep
one vane in place. Express your answer in terms of ρ, a, p1, p2, V1, β1 and β2.



2. Relevant equations
bernoulli equation
newton equation of momentum: mass flow out X velocity 2 - mass flow in X velocity 1= forces acting on Control volume.


3. The attempt at a solution
I find in the x-direction ( assuming unit depth): rho X a X V²₂cos (beta 2) - rho X a X V²₁= (p₁-p₂)X a + F_x.
I think F_y=0 but i'm not sure so please help i've spent hours on this

Attached Files

PS4.pdf (66.3 KB, 8 views)