8.2 A flat strip of metal emerges from a liquid bath of viscosity no and pressure p; above ambient and has velocity ч on passing through a slot of the form shown in the sketch. In the initial convergent part of the slot the film thickness decreases linearly from ho + s to ho over a length en, on each side of the strip. In the final section of the slot the film on each side of the strip has a constant thickness ho over a length l (1 — ns). - P = Pi Sp P=P; ho Up no -p=0 State clearly the boundary conditions required to determine the pressure distribution along the slot length in the sliding direction on the assump-/ntion that the liquid is isoviscous and incompressible and the slot is in- finitely wide. Sketch the pressure distribution along the x axis and show that the volume flow rate per unit width % on each side of the strip can be written in dimensionless form as 29 UbSh = (H³P;/3) (H。 + 1)² + 2H。 (H。 + 1) (1 + H。 − ns) n¸H。 (2H。 + 1) + 2(1 - ns) (H。 + 1)² where P₁ Pis noul ho and Ho = ᎦᏂ Demonstrate that for P; equal to zero the expression for Q reduces to forms appropriate to the parallel-surface and fixed-incline-surface bearing situations as ns approaches zero and unity, respectively. 1 Determine the minimum value of P required to ensure that the peak pressure in the slot is located at the inlet, where h = hosh if ns and Ho=1. 2

Fig: 1

Fig: 2