Basic fluid mechanics of sled question

In summary, a sled sliding on a thin layer of water between ice and runners exerts a horizontal force of 1.2 lb at a speed of 50 ft/s. With a total contact area of 0.08 ft^2 and a water viscosity of 3.5(10^-5) lb*s/ft^2, the thickness of the water layer can be determined using the equation h = (viscosity)*Umax/h, which results in 1.17(10^-4) ft according to the book. However, it is possible that the book may have a mistake as this use of scientific notation is unusual.
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stinlin
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Homework Statement



A sled slides along on the snow on a thin horizontal layer of water between the ice and the runners. The horizontal force that the water puts on the runners is equal to 1.2 lb when the sled's speed is 50 ft/s. The total area of both runners in contact with the water is 0.08 ft^2, and the viscosity of the water is 3.5(10^-5) lb*s/ft^2. Determine the thickness of the water layer under the runners. Assume a linear velocity distribution in the water layer.

Homework Equations



Shear stress = viscosity * (du/dy)

du/dy is the rate of strain.


The Attempt at a Solution



Well, because it has a linear velocity distribution, du/dy = Umax / h, where Umax is the maximum velocity and h is the height or depth of the fluid.

Umax = 50 ft/s
Max shear stress = P/A = 1.2 lb / 0.08 ft^2 = 15 lb/ft^2

So rearranging with substitutions, the equation looks like this:

h = (viscosity)*Umax/h

With numbers:

h = (3.5(10^-5) lb*s/ft^2) * 50 ft/s / 15 lb/ft^2 = 0.00175/15 ft

h = 11.7(10^-5) ft

That seems legit, no? But my book says 11.7(10^-4) ft. Now I know I shouldn't ALWAYS trust the book, but I just have a feeling I missed something if I'm off by only one order of magnitude. Thoughts?
 
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  • #2
stinlin said:
my book says 11.7(10^-4) ft.
That is an unusual use of scientific notation. Are you sure it doesn’t say 1.17(10^-4) ft?
 
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What is fluid mechanics?

Fluid mechanics is a branch of physics that studies the behavior of fluids, which include liquids and gases, and the forces acting on them.

How does fluid mechanics apply to sleds?

Fluid mechanics is important in understanding the movement of a sled because it helps to explain the forces acting on the sled as it moves through a fluid, such as air or snow. This knowledge can be used to design a sled that minimizes drag and maximizes speed.

What is drag force?

Drag force is a force that opposes the motion of an object through a fluid. It is caused by the interaction of the fluid molecules with the surface of the object, creating a resistance to its movement.

How does the shape of a sled affect its performance?

The shape of a sled can greatly affect its performance because it determines the amount of drag force acting on the sled. A streamlined shape with minimal surface area will experience less drag, allowing the sled to move faster and more efficiently through the fluid.

What other factors besides shape can impact a sled's performance in fluid mechanics?

Other factors that can impact a sled's performance in fluid mechanics include the material of the sled, the surface it is sliding on, and external forces such as wind or gravity. These factors can influence the amount of drag force acting on the sled and affect its speed and stability.

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