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## Homework Statement

A horizontal water jet produces a wide sheet of parallel-flowing liquid that strikes an inclined plate and then divides, with a fraction of the liquid flowing up the plate and the remainder flowing down the plate. The figure shows a section of the flow. All surfaces of the liquid are exposed to atmospheric pressure and both the gravity forces and frictional losses in the flow may be neglected.

Shear stress between the plate surface and the liquid may be neglected in comparison with pressure forces there and, therefore, the force between the plate and the liquid is perpendicular to the plate surface with zero component tangent to the plate surface.

With these facts, use mass and momentum balances to:

a) Determine the relation between the fraction of the liquid that travels up along the plate and the angle θ.

## Homework Equations

Bernoulli's equation { u

_{1}=u

_{2}=u

_{3}}

Conservation of mass {m

_{1}=m

_{2}+m

_{3}

Conservation of momentum {um

_{1}=um

_{2}+um

_{3}

## The Attempt at a Solution

F

_{x}:

um

_{2}cos(θ)-um

_{3}cos(-θ)-um

_{1}=0

F

_{y}:

um

_{2}sin(θ)-um

_{3}sin(-θ)=0

m

_{2}=-m

_{3}--> can not be true