# Homework Help: Mass Flow of Snow while Plowing?

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1. Jul 1, 2015

### BabyHuey06

1. The problem statement, all variables and given/known data
Lets say I am plowing snow in a straight line using a standard V-plow. The angle of the V between both blades is 130 degrees. The coefficient of kinetic friction between the blades and the snow is about .1. The speed of the plow is 5 mph or 2.2 meters per second. The cross-sectional area of the front of the plow is 2 meters wide by .5 meters tall. The plow itself has a cross sectional geometry of a semi circle with a radius of .25 meter.

The density of the snow is 300 kg/m^3. The cross-sectional area of the swath of snow is 2 meters wide by .25 meters tall.

What will be the mass flow of snow both into and out of the plow?

Because the plow is moving at such a slow speed. Assume that the snow accumulates to fill the snow plow before any snow leaves the plow.

2. Relevant equations
mass flow = density x velocity x cross-sectional area
All other physics equations for kinematics

3. The attempt at a solution
The mass flow into the plow = (300 kg/m^3) x (2.2 m/s) x (2m x .25m) = 330 kg/s

The mass flow out of the plow = ?????? I don't know how to find it

2. Jul 1, 2015

### SteamKing

Staff Emeritus
Once the snow fills the plow and starts to leave, where does any new snow picked up by the plow go?

3. Jul 1, 2015

### BabyHuey06

So the snow is just being pushed off to the side and onto the freshly fallen snow that isn't being plowed. There is a wall of snow next to plow which is why the snow accumulates inside the plow before leaving.

4. Jul 1, 2015

### haruspex

It's not clear to me whether you have understood and accepted SteamKing's point. In steady state, mass rate in = mass rate out.

5. Jul 2, 2015

### BabyHuey06

Oh haha that's what he was trying to say. Whoops, sorry about that. So it is not at steady state. Snow accumulates in front of the plow and does not go anywhere. What I think I need to do is figure out where the snow would most logically and theoretically leave the plow. That would give me the cross sectional area. Then knowing how fast the plow is moving and the geometry of the plow I should be able to somehow figure out how fast the snow is exiting the plow?

6. Jul 2, 2015

### BabyHuey06

Update 1:
The moving snow is not at a steady state in terms of mass flow. Snow gradually builds up in front of the plow, accumulating mass.

7. Jul 2, 2015

### haruspex

But that will vary over time. The exit rate will gradually increase until it matches flow in.

8. Jul 2, 2015

### BabyHuey06

How so? Wouldn't the snow eventually accumulate to the point where it can no longer be pushed, if there was a max amount of power that can go into it.

How do you know that the exit rate will eventually match the intake?

9. Jul 2, 2015

### haruspex

If it is going to build up to the point where the snow plow comes to a halt then it's not much of a snow plow. The whole point of the plow design is to prevent that (though I suppose there is a limit to the depth of snow a given plow can cope with).
Besides, merely having accumulated a pile of snow of mass m does not give you a basis for saying the plow has to work any harder. That pile is moving at the same speed as the plow.