2. A thin 30cm x 30cm flat plate is pulled at 4. 22 m/s horizontally through a 3.9 mm thick oil layer sandwiched between two plates, one stationary and the other moving at a constant velocity of 1.8 m/s, as shown in the Figure 2. The dynamic viscosity of the oil is 0.027 Pa.s (N.s/m²). Assuming the velocity in each oil layer to vary linearly, a. plot the velocity profile and find the location where the oil velocity is zero, b. determine the force that needs to be applied on the plate to maintain this motion. Fixed wall h = 1.2 mm V = 4. 22 m/s F h = 2.7 mm V = 1. 8 m/s Moving wall Figure 2

The velocity distribution in a 25 m long and 40-cm diameter pipe is v(r) = 2*(1-25r²) where the velocity units are m/s and radius is in m. Determine the following: (a) What is the drag force (i.e shear force) on the wall for water with an absolute (i.e., dynamic viscosity) of 0.0010 kg/m-s? (b) What is the shear stress at a distance of 5 cm from the centerline of the pipe? R-0 R r=0

Two plates are positioned at distance of 1.3 mm from each other. One of the plates is moving at velocity of 0.5 m/s; the movement requires a shear stress of 5 N/m². Calculate dynamic viscosity of the fluid between the plates by assuming linear velocity distribution. Round off the answer to three decimal digits in kg/ms, but enter the answer without the unit. Answer:

A torque is applied to rotate a cylindrical shaft (diameter D 1 , length L) at a constant angularspeed ω, inside a co-axial, stationary cylinder of the same length and diameter D 2. The gapbetween the bottom surface of the shaft and that of the stationary cylinder is h.(a) Develop a general expression of the torque in terms of the geometric dimensions andthe viscosity μ of an oil filling the gaps between the shaft and the stationary cylinder.Assume linear velocity profiles in all the gaps.(b) Determine the numerical value of the torque in the case of an oil of viscosity of 0.1Pa.s. [D 1=5cm, D 2=5.2cm, L=10cm, ω=50rpm, h=1mm]