4H Extra Material

Question 1

State the Froude number

Answer 1

v1/ sqrt(g h1)

Question 2

What does the Froude number tell us about hydraulic jumps?

Answer 2

Fr = 1 - no jump
Fr < 1 - h2 < h1, negative jump
Fr > 1 - h1 < h2, positive jump

Question 3

State the shallow water equations

Answer 3

∂_t v + v⋅∇v = -g∇h
∂_t h + ∇⋅(hv) = 0

Question 4

How does the shallow water differ from the standard water model

Answer 4

Still incompressible; not irrotational.

Question 5

How do we find the pressure component in shallow water waves?

Answer 5

Consider the z-component of momentum, where all velocity = 0 and we obtain an ode for pressure. Solve for p=0 at surface