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

AI Thread Summary
The discussion focuses on the Coriolis effect's impact on river water levels, specifically how the west bank is lower than the east bank. The proposed formula for this difference is 2Dwvsin(lambda)/g, where w is Earth's angular velocity and lambda is the latitude. A participant attempts to derive this result but struggles with proving their calculations and simplifying the equation. They express uncertainty about their approach and seek validation from others. The conversation highlights the complexities of applying physics concepts to real-world scenarios, particularly in fluid dynamics.
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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?
 
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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?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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