Foundations of Fluid Mechanics Tutorial 1- on Viscosity, Surface Tension Q (1*) The velocity distribution for laminar flow between parallel plates is given by: 2max2 1 = h yU U where h is the distance separating the plates and the origin is placed midway between the plates. Consider flow of water at 15C with maximum speed of 0.05 m/s and h=5 mm. Calculate the force on a 0.3 m2 section of the lower plate and give its direction. From Tables, = 1.14x10 -3 Ns/ m2 Q (2) A female freestyle ice skater, weighing 112 lbf, glides on one skate at speed V = 20.5 ft/s. Her weight is supported by a thin film of liquid water melted from the ice by the pressure of the skate blade. Assume the blade is L = 11.5in. long and w = 0.125in. wide, and that the water film is h = 0.0000575 in. thick. Estimate the deceleration of the skater that results from viscous shear in the water film, if end effects are neglected. From Tables, = 3.66x10 -5 lbf s/ ft2 Q (3) A concentric cylinder viscometer may be formed by rotating the inner member of a pair of closely fitting cylinders. For small clearances, a linear velocity profile may be assumed in the liquid filling the annular clearance gap. A viscometer has an inner cylinder of 75 mm diameter and 150 mm height, with a clearance gap width of 0.02 mm. A torque of 0.021 N.m is required to turn the inner cylinder at 100 rpm. Determine the viscosity of the liquid in the clearance gap of the viscometer. Q (4*) A conical pointed shaft turns in a conical bearing (as shown in FIG 1). The gap between shaft and bearing is filled with heavy oil having the viscosity of SAE 30 at 30C. Obtain an algebraic expression for the shear stress that acts on the surface of the conical shaft. Calculate the viscous torque (T) that acts on the shaft. From Tables, = 0.2Ns/ m2 (Hint : To start with, S.T. 2 cos tan3 4 a H T = ). FIG 1 Q (5*) A child produces soap bubbles using a tube of diameter 1 mm. What is the maximum over pressure that he should exert to get good bubbles ? From Table, Surface tension = 2x10-2 N/m Q(6*) Blood sample is drawn into a fine glass capillary of diameter 1mm, by touching one end of it to a freshly pictured fingertip. If the surface tension of blood is approximately = 5x10-2 N/m and its contact angle with glass is 0 and its density 1056 kg/m3, estimate the volume of blood sample drawn.