Question

Problem 1: A Newtonian fluid is confined between the plate and a fixed surface. If the velocity profile is defined by u =(8y-0.3y) mm/s, where y is in mm, determine the force that must be applied to the plate to cause this motion. The plate has a surface area of 15 (10) mm in contact with the fluid. Use u = 0.482 (10) N.s/m(20 points) (8y-3.3y) du -0 T = Muy 72 (0.482 +5%) (8- 0.64) = 0.46212"(8-0.660)) = 0.003856 Pa TI 0.482x153/8-06 (amm) = 0.00 2699 Pa 9 @ bottom 2.003856 = 15 x 103 m² = @ Top - 2.50 2699 Pho ne F = 57.84 N F = 40.488 ~ X 1-2
answer is 4.05(10^-5) N

Answer 1

Here le= 0.482 x 100% N-s. ma - 0:482 xlo? N -s mma los mma = 0.482 x 10 9 N -s Now that by osy 1. u= sy. 0.3y² du =8-0.by at y = 4mm, 8-(0.6x4) = 5.6 mmis mm know - 0.402 - - x6 '; 15.6 15 x 5.6 we know ta lex du over or fee that lo-95.6 - 2.6992 - = boty AB 10 9 Tsx163 F: 40.488x10-6 N F- 4.05 x 100% NI os