Question

Pantaw2 Spring 2020 - MAE 301 Pluid Mechanics Chapter 2: Properties of Fluids Due date: Wed,Fab. 20 Points. Problem 1 A metal plate 1.25 mm 125 mm x 8 mm thick and weighing 90 N is placed midway in the 24 mm gap between the two vertical plane surface. The gap is Miled with an oil of specific gravity 0.85 and dynamic viscosity 3.0 N/m2 Determine the force required to lift the plate with a constant velocity of 0.15 m/s. _120 Points. Problem 2 The velocity distribution for flow over a plate is given by v = (2 y-y) where v is the velocity m/s at a distance y meters above the plate. Determine the velocity gradient and shear stress at the boundary and 0.15 m from it. _/20 Points. Problem 3 A soap bubble 62.5 mm diameter has an internal pressure in excess of the outside pressure of 20 N/m2. What is tension in the soap film? 120 Points- Problem 4 A drop of water at 20°C is forming under a solid surface. The configuration just before separating and falling as a drop is shown in the figure. Assume the forming drop has the volume of a hemisphere. What is the diameter of the hemisphere just before separating?

Answer 1

NOTE: In problem 1 the size of the plate should be 1.25m×1.25m×6mm not 1.25mm ×1.25mm × 6mm.The below problem is solved for all dimension of the plate in 'mm' only as mentioned in problem.

Solution to first problem] [Problem 1 Gilven metal plate (1-25X1-25x6 ) mm3 : Volume of plate = 9.375 mm?:v .:TV = 9.375X10-9m=? 111111ܠ1ܠܠܠܠܠܪ ums Weight of plate = WE GON Smm 6mm 9 mm For oil Specific gravity = 0.85 . density: P - 0.85Xlow = 850 kg/m² - - 3 N.s|m V= 0.15 ms. oli gap on each side of platesh: 9mm - grlom. To find force required to lift the plate (F) Tsolution FBD of the plate gives: FB +F: WF ." - Es = shear force (viscowon ) One side of plate FB = Buoyancy) :: F= W + 2 55 - 50 Te Pay- 850X9.81x 9 - 375X10-9 7817X10-SN FS: MAYA {By Newton's law of viscosity, Assumina linear velocity profile for oil in the gap]

:: Fs- 3 x 6.25x1.25 xio-6 m2) x 0.15 9X10-3 [Fs = 7.8125 Xlo-sn :. F= w +2 Fs - FB o go + 2X 7.8125 Xlo-S -7.817X10 5 :-Fe gon