Ball Bearing Ø/mm 1.59 2.38 3.175 Golden Syrup 200- 175 mm - N/A - 135.92 89.36 175-100 mm - N/A - 432.68 Time to fall marked distance (/s) Washing up liquid 268.25 100- 25 mm 15.19 3.18 3.79 Table 1 25-0 mm 4.21 1.91 1.09 100 - 25 mm 2 0.47 Olive oil 0.21 25-0 mm 1.31 0.21 0.14 Exercise B - Measurement of Viscosity Objective To determine the viscosity of various liquids at atmosphere pressure and temperature. Background theory Viscosity is a measure of a fluid's resistance to flow. It describes the internal friction of a moving fluid or can be described as the friction that a fluid will exert on an external object as travels in that fluid medium. The theory behind this experiment is as follows: From the Figure 2; when the ball is moving with a uniform velocity u, then forces acting on the sphere are: a. the gravitational force on the ball mg. b. the buoyant force or upthrust FB c. the viscous force resisting motion Fy Since the velocity of fall is uniform, then algebraic sum of these forces must be zero. mg - FB-Fv=0 The gravitational force on the ball can be calculated as: 4 mg = Ps9 3 where Ps= density of ball, r = radius of sphere. The buoyant force can be calculated as: 4 FB = P193 P193 πr.² πr² where P1 = density of liquid. Fv=6yX₂ The viscous force from Stokes Law can be calculated as: Where μ = coefficient of viscosity, u = mean velocity of ball. 4 μ = - Ps9²₁². Results 4πr³g 3x6πμru u= == 쓰 V = Calculate the velocity of the ball passing through the marked distances (between 100 to 25 and 25 to 0) using Equation 4 and find the average. Distance through which ball falls Time 4 Liquid Water πρ3 – 6πμru = 0 Calculate the average Dynamic viscosity for three different diameter balls passing through each liquid. Complete Table 3 for Dynamic Viscosity. Calculate Kinematic Viscosity by considering density of the liquids found in the first experiment A (Table 2) using the following equation: (Ps - P₁) = ²/r² g (Ps-P₁) u Barometric pressure 774.0635 mm Hg. Temperature 16°C. Specific gravity of steel: 7.8 Olive oil washing up liquid Golden Syrup Equation 3 Table 3. Results for Dynamic and Kinematic Viscosity Dynamic Viscosity, μ (kg/ms) Using equation 3 Equation 4 Equation 5 Kinematic Viscosity, v (m²/s) Using equation 5

List the various types of fluid. Define kinematic viscosity and compressibility. Note the expression of capillary fall as well.

Find the dynamic and kinematic viscosities of kerosene, SAE 10W-30 motor oil, and water at a temperature of 38°C (100°F). show solution.

Question 1: Define and state the viscosity equation for a Coutte flow. Question 2: Develop and algebraic equation for viscosity of a liquid as a function of temperature. Calculate the kinematic viscosity of water at T = 303 K. Question 3: If a liquid water at 300C is flowing in a pipe and the pressure drops to the vapor pressure, what happens in the water and why, explain?

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A shaft of diameter 0.35 m rotates at 200 r.p.m. inside a sleeve 100 mm long. The dynamic viscosity of lubricating oil in the 2 mm gap between sleeve and shaft is 8 poises. Calculate the power lost in the bearing.

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Problem 2 The apparatus sketched in the figure below serves as a viscometer i.e. it can be used to measure the viscosity of a liquid. In the drawing, D is a large reservoir containing a viscous liquid A and E is a cylindrical tube of radius R, open at both ends, surrounding and coaxial with B, which is a cylindrical "bob" of radius êR that is dragged up through the fluid by a frictionless pulley system (C) utilizing a weight W. Determine a design equation that relates the viscosity of the liquid to the geometry of the system and the weight W. Hint: you can assume that the length of the cylindrical tube is sufficiently long for the flow to reach steady state. W E D B

2.4-2. Shear Stress and Shear Rate in Fluids. Using Fig. 2.4-1, the lower plate is being pulled at a relative velocity of 0.40 m/s greater than the top plate. The fluid used is water at 24°C. a. How far apart should the two plates be placed so that the shear stress t is 0.30 N/m^2? Also, calculate the shear rate. b. If oil with a viscosity of 2.0 x 10^-2 Pa•s is used instead at the same plate spacing and velocity as in part (a), what is the shear stress and the shear rate?