During a coating process, a thin, flat tape of width w is pulled through a channel of length L containing a Newtonian fluid of density ρ and dynamic viscosity μ . The fluid is in contact with both sid

Question

During a coating process, a thin, flat tape of width w is pulled through a channel of length L containing a Newtonian fluid of density $ρ$ and dynamic viscosity $μ$ . The fluid is in contact with both sides of the tape. Estimate the force required to pull the tape through the channel if the tape has velocity V and the channel has height H. You may assume that the tape is much thinner than H and tape is in middle of channel.

Question figure

TestHub · Accepted Answer

The tape has wetted area wL on each side; each fluid gap is H/2.

$\frac{d v}{d y} ≃ \frac{V}{H /2} = \frac{2 V}{H}$

$τ = μ \frac{2 V}{H}$

$A_{both sides} = 2 w L$

$F = τ A_{both sides}$

$F = \frac{2 μ V}{H} (2 w L)$

$F = \frac{4 μ V w L}{H} (A)$

Physics - Fluid Question with Solution | TestHub

Options:

Doubts & Discussion