Figure P6.4 depicts pressure-driven flow in a horizontal parallel-plate channel with wall spacing H, length L, and width W (not shown). This is called plane Poiseuille flow. Assuming that the flow is steady, laminar, and fully developed with a mean velocity u, the local velocity is found to be (Example 7.2-1)

(a) Calculate each component of τ for this flow.

(b) Use a force balance on the control volume in Fig. P6.4 to evaluate the difference between the average pressures at surfaces S₃ and S₄ (x = 0 and x = L, respectively). In using the results from part (a), be careful with the directions of the four unit normals and with the algebraic signs.

Transcribed Image Text:

2,0) = 6 [G) - G)]. (y) 6u y S3 X U₂ = 0) = V₂. S₁ S₂ H S4 (P6.4-1) g L Figure P6.4 Plane Poiseuille flow in a horizontal channel. The control volume for an overall force balance is shown by the dashed lines.