You want to predict how fast a glacier that is $200 \mathrm{ft}$ thick will flow down a slope inclined $25^{\circ}$ to the horizontal. Assume that the glacier ice can be described by the Bingham plastic model with a yield stress of $50 \mathrm{psi}$, a limiting viscosity of 840 poise, and a SG of 0.98 . The following materials are available to you in the lab, which also may be described by the Bingham plastic model:

	Yield Stress $\left(\mathbf{d y n} / \mathbf{c m}^{2}\right)$	Limiting Viscosity $(\mathbf{c P})$	SG
Mayonnaise	300	130	0.91
Shaving cream	175	15	0.32
Catsup	130	150	1.2
Paint	87	95	1.35

You want to set up a lab experiment to measure the velocity at which the model fluid flows down an inclined plane and scale this value to find the velocity of the glacier.

(a) Determine the appropriate set of dimensionless groups.

(b) Which of the above materials would be the best to use in the lab? Why?

(c) What is the film thickness that you should use in the lab, and at what angle should the plane be inclined?

(d) What would be the scale factor between the measured velocity in the lab and the glacier velocity?

(e) What problems might you encounter when conducting this experiment?