2.2 Fluid (2.2.20) The signature dish of the world-famous French Laundromat rest

Question

2.2 Fluid (2.2.20) The signature dish of the world-famous French Laundromat restaurant is the bologna honey-molasses sandwich. The sandwich, shown in cross-section below, includes a square piece of bologna which is 12 cm on each side and 3.0 mm thick. The bologna is between two pieces of bread with the same dimensions as the bolo is a layer of molasses with viscosity 5000 cP. Between the bologna and the bottom piece of bread is a layer of honey with viscosity 10000 cP. The distance between the top and bottom layers of bread is 6.00 mm. A diner attempts to remove the bologna from the bread by holding the two slices of bread in place and applying a 13N force to the bologna. The result is that the bologna begins to slide out from between the slices of bread at 5 cm/s. Given that the honey layer must be thicker than the molasses layer in order for the flavors to balance, what is the thickness of the molasses layer? The sandwich is shown in cross section below ics (with viscosit gna. Between the bologna and the top piece of bread molasses 3.00 m 6.00 mm

Explanation / Answer

Force of viscosity = viscosity constant * area of cross section * change in velocity / change in depth

assumed thickness of molasses layer = a

assumed thickness of honey layer = b

Change in velocity with depth through molasses as well as honey is 5 cm/s as the bread is being held stationary while bologna moves with 5 cm/s velocity

Force of viscosity on bologna by molasses = 50 Poise * 12^2 * 5 / a dyne = 36000/a dyne

Force of viscosity on bologna by honey = 100 * 12^2 * 5 / b dyne = 72000/b dyne

Total force = 13 N = 1300000 dyne = force by molasses + force by honey = ( 50 Poise * 12^2 * 5 / a ) + ( 100 Poise * 12^2 * 5 / b ) = 1300000 dyne

Finally, a + b = 0.3 cm

solving the above two equations for a and b and remembering that b > a (since thickness of honey > thickness of molasses) and hence picking the smaller value for a from the quadratic,

36000/a + 72000/(0.3-a) = 1300000

reduces to 1300a^2 - 354a + 10.8 = 0

choosing the smaller value of a since a has to be less than b,

a = 0.035 cm & b= 0.265 cm

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