Question

Example 3.5 A viscous and incompressible non-Newtonian fluid with a density of $\rho$ is flowing through a wide flat channel with a height of 2h. At a certain section of the channel, the velocity distribution is given by $u = U_c[1 - (y/h)]$ for $0 < y < h$, as shown in the figure, where $U_c$ is the velocity at the centerline of the channel. Determine the mass flow rate per unit width, volumetric flow rate per unit width and average velocity. Solution

          Example 3.5
A viscous and incompressible non-Newtonian fluid with a density of $\rho$ is flowing through a wide flat
channel with a height of 2h. At a certain section of the channel, the velocity distribution is given by
$u = U_c[1 - (y/h)]$ for $0 < y < h$, as shown in the figure, where $U_c$ is the velocity at the centerline of the
channel. Determine the mass flow rate per unit width, volumetric flow rate per unit width and average
velocity.
Solution

Example 3.5
A viscous and incompressible non-Newtonian fluid with a density of ρ is flowing through a wide flat
channel with a height of 2h. At a certain section of the channel, the velocity distribution is given by
u = Uc[1 - (y/h)] for 0 < y < h, as shown in the figure, where Uc is the velocity at the centerline of the
channel. Determine the mass flow rate per unit width, volumetric flow rate per unit width and average
velocity.
Solution

Added by Gregory E.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

08/02/2023

Step 1

Step 1: Calculate the mass flow rate per unit width (ṁ): The mass flow rate per unit width can be calculated using the formula: ṁ = ρ * ∫(u * dy) from 0 to h Substitute the given velocity distribution u = Uc[1 - (y/h)] into the formula: ṁ = ρ * ∫(Uc[1 - (y/h)] Show more…

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Example 3.5 A viscous and incompressible non-Newtonian fluid with a density of ρ is flowing through a wide flat channel with a height of 2h. At a certain section of the channel, the velocity distribution is given by u = Uc[1 - (y/h)] for 0 < y < h, as shown in the figure, where Uc is the velocity at the centerline of the channel. Determine the mass flow rate per unit width, volumetric flow rate per unit width, and average velocity.