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

[gikwiye]

Homework Statement

µ

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.

Homework Equations

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

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

 

[mark726]

problem and I'm still not sure

your first step in responding to this forum post would be to clarify any uncertainties or questions you have about the problem. This could involve asking for clarification on the given information, such as the meaning of "station" or the assumptions made about the fluid. It could also involve asking for more specific information, such as the dimensions of the vanes or the units of measurement used for the velocities and pressures.

Once you have a clear understanding of the problem, you can then begin to work on a solution. In this case, you could start by applying the Bernoulli equation and the Newton equation of momentum to the given information. From there, you can use algebraic manipulation to solve for the unknown variables and ultimately find the horizontal and vertical components of the force necessary to keep one vane in place.

It is also important to note any assumptions or simplifications made in your solution, as these can affect the accuracy of your results. Additionally, it may be helpful to double-check your calculations and ensure that your final answer is in the correct units for force.

In conclusion, as a scientist, your approach to this forum post would involve clarifying any uncertainties, applying relevant equations, and clearly presenting your solution and any assumptions made.