Two plates are initially at rest and that one of the plates suddenly starts movi

Question

Two plates are initially at rest and that one of the plates suddenly starts moving in a direction parallel to its surface with velocity v. The plates are separated by a distance d and filled with a fluid of viscosity and density .

a. We’d like to know how long we have to wait for steady state conditions to be established. To do this, we can estimate a characteristic time constant for this system. Combine the quantities , , and d to create a new quantity with units of time. This will be the characteristic time tc associated with the development of steady state flow conditions.

b. What is the value of the characteristic time for the development of steady state flow in a system in which liquid Al at 750 °C flows between plates separated by 2 mm?

Explanation / Answer

Time constant involving viscosity(µ), density() and diameter(D) is given by

Time constant, = (*d2)/µ

The units of time constant is seconds.

Density of liquid aluminium at 750°C is 2350 kg/m3 and viscosity of liquid aluminium at 750°C is 1.5×10-3 Pa.s

Thus the Characteristic time constant for liquid aluminium at 750°C is

= {2350 * (2×10-3)2}/1.5×10-3 seconds

===> = 6.267 seconds

Thus the characteristic time constant for liquid aluminium at 750°C for the development of steady state flow is = 6.267 seconds

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