How Does the Coriolis Effect Influence River Water Levels at Different Banks?

[karnten07]

Homework Statement

A river of width D flows Northward with speed v. Show that the water is lower at the west bank than at the east bank by approximately

2Dwvsinlamda/g

where w is the angular velocity of the Earth and lamda the latitude.

Homework Equations

The Attempt at a Solution

I get the difference in height as 2Dwvsin(lamda)cos(lamda)/sqrt(g^2 +(2wvsin(lamda)cos(lamda))^2)

So if this was the same as my answer it would mean that cos(lamda)/sqrt(g^2 +(2wvsin(lamda)cos(lamda))^2) = 1/g

Im just unsure how to prove this, it looks like a simple right angled triangle to show this by rearranging to show coslamda = sqrt(g^2 +(2wvsin(lamda)cos(lamda))^2)/g

Does this look right guys?

 

[Shooting Star]

Not really. You can't reduce your formula to the answer through any approximation that I can see. Why don't you just share your calculations with us?