Homework #8 GEOL 4880 Humphrey Fall 2016

Please make your homework somewhat neat and readable!!

Question 0: Tell me your term paper Idea, include the landform, where it is, and say a little about what you are planning to do/say about it?

1 Calculate for the Laramie River

· Basal shear stress

· Shear velocity, U_*

· Thickness of the viscous sub layer near the bed

2 Estimate Reynolds numbers (to describe the state of turbulence) appropriate to:

· the Laramie River,

· the weather (atmosphere) above Laramie,

· a cup of coffee as you add cream,

· a water squirt gun nozzle,

· a swimming amoeba.

· And a hard question, a grain of 0.5mm sand on the bed of the Laramie RIver,

3 Reproduce the argument for Stoke’s Law for settling velocity, and therefore reproduce the Stoke’s equation (minus the value of the coefficient). You might find it useful to follow the following line of logic:

· Gravity force on particle

· A scale for the viscous shear stresses on the particle surface

· Total drag force on particle due to surface shear stress times the surface area

· Balance gravity and viscous drag to get Stoke’s Law (with an incalculable constant)

4 a) What is the order of magnitude of the lift force on a 1cm diameter piece of gravel on a river bed, with a 0.5m/s water flow over it and stagnant water under it. Use the Bernoulli equation we developed in class. Is the force enough to lift the particle? (to get a scale for the lift force from the Bernoulli effect, you can assume the water velocity difference is the full 0.5m/s) [hint: the Bernoulli equation gives you a way to calculate the water pressure; that water pressure can be turned into a force by multiplying by the cross-sectional area of the particle]

b) If the particle in ‘a’ gets up into the flow, in what direction (up or down) will the Bernoulli lift try to move the particle? You may assume the particle has not been accelerated up to the full flow speed, and that the flow is a shear flow, i.e. faster at the surface than the bed.

5 (this weeks geomorphic puzzle) Many lakes in cold regions of the world turn-over. The phrase describes a phenomena that occurs once (or twice) a year; the water in the lake moves so that in a short time the water at the top of the lake sinks and flows under the water at the lake bottom, while the water that was at the bottom circulates onto the top of the lake. This process is hugely important for nutrient cycling. Why does it occur, where does the head gradient come from? If you can, explain why the event is often sudden, not gradual, and why it doesn’t occur in warmer regions. And as a bonus, why doesn’t the ocean do the same thing. (hint: think of temperature and density gradients)