2. The Reynolds number for a particular microchannel flow is found to be Re = 2. a. If all channel dimensions (length, width, and height) are reduced by a factor of 10, and the time required for a particle to traverse the length of the channel is invariant, what is the value of Re for the smaller channel? b. If the flow velocity is constant for both channels, rather than the time scale, what is the value of Re for the smaller channel? Solution Initial Case Re = rho*V*L/mu = 2 Time req to travel the distance t = L/V------(1) a) When dimensions are reduced by 10 L1, W1, H1 L1 = L/10 W1 = W/10 H1 = H/10 Time required to travel the distance L1 is t = L1/V1-----(2) Given 1 = 2 L1/V1 = L/V (Since L1 = L/10) V1 = 0.1*V Re = Rho*V1*L1/mu = (1/00)*rho*V*L/mu = 0.02 b) Now Velocity remains constant Re = rhi*V*L1/mu =0.1*rho*V*L/mu = 0.2 .

1. 2. The Reynolds number for a particular microchannel flow is found to be Re = 2.
a. If all channel dimensions (length, width, and height) are reduced by a factor of 10, and
the time required for a particle to traverse the length of the channel is invariant, what is
the value of Re for the smaller channel?
b. If the flow velocity is constant for both channels, rather than the time scale, what is the
value of Re for the smaller channel?
Solution
Initial Case
Re = rho*V*L/mu = 2
Time req to travel the distance
t = L/V------(1)
a)
When dimensions are reduced by 10
L1, W1, H1
L1 = L/10
W1 = W/10
H1 = H/10
Time required to travel the distance L1 is
t = L1/V1-----(2)
Given

2. 1 = 2
L1/V1 = L/V (Since L1 = L/10)
V1 = 0.1*V
Re = Rho*V1*L1/mu = (1/00)*rho*V*L/mu = 0.02
b)
Now Velocity remains constant
Re = rhi*V*L1/mu =0.1*rho*V*L/mu = 0.2