Part 1: Rotating Viscometer One type of viscometer involves the use of a rotating cylinder inside a fixed cylinder as shown in the figure below. The gap between the cylinders must be very small to achieve a linear velocity distribution in the liquid. Design a viscometer that will be used to measure the viscosity of motor SAE 30 oil from 0°C to 100°C. Here you need to determine and report the following parameters: a. The dimensions of the two cylinders, lengths, thicknesses and diameters. b. The gap clearance between the surfaces of the cylinders. c. The rated power of the driving motor. d. The rotational speed of the shaft. e. Assumptions, and operational procedure. Rotating Drum Viscometer Drive Motor Rotating Cylinder Viscos Liquid Sample Stationary Cylinder Figure 3: Schematic for task 3 part 1. Part 2: Viscosity Correlation For the above viscometer: a. Calculate the applied power function of the oil viscosity over the specified range of temperature. Plot Power function of viscosity. b. Fit the viscosity function of temperature of the above motor oil to the following logarithmic quadratic correlation as described below. Find the values for the constants a, b, and c. Take Ho at To =0 °C. In - a + b In4.

n = Xe()r -------Equation 1 where X = 1.7419 and (E/R) = -0.018 are constants for a given fluid. You are required to carry out appropriate calculations on the effect of changes in temperature given in table A by using equation 1 for Ethanol on the viscosity of a fluid. Table A NO Temperature viscocity n T°C cP 10 3 20 30 5 40 6. 50 7 60 8 70 In addition to this, calculate other constraints such as the variety of shear stress (T) and force due to fluid viscosity, when the two layers of different compressible Newtonian fluids are contained between two flat plates separated by a distance of 0.05m and fluid moving with the velocity of 2m/s in the horizontal direction. Assume the shear area between the fluid layers is 0.5m². To do this you required to explain, with examples, the effects of temperature and shear forces on Newtonian and non-Newtonian fluid. Also, explain the operation and constraints of different viscometers that quantify viscosity in fluids. 2.

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?

f. A study of the physical characteristic of honey was conducted due to the large demand of royal jelly. A capillary tube viscometer was used by a researcher in determining the viscosity of the honey. The viscometer is 250 mm long with an outside diameter of 55mm and effective thickness of 2.5mm and was used horizontally so that the effect of gravity was neglected. At an ambient temperature of 30°C the following data were collected: Q (cc/s) 1.25 1.55 1.80 2.05 ДР (Ра) 10.0 12.5 15 17.5 20.0 2.55 What will be the stress produced per unit length in the tube used in the production of royal jelly if it has a radius of 5mm and a flow of 1 capsule per second. (1 capsule = 0.85 cc of royal jelly).

b

Please solve in simplest terms

B1. Determine the kinematic viscosity of the fluid between the plates as shown in Figure B1 given the following information: F = 5N h = 0.5mm v = 7m/s L=21 cm w = 10cm SG= 0.80 Moving plate Stationary plate Fluid Figure B1 V

Problem 3: A honeybee farmer wants to measure the absolute viscosity of his honey. You suggest dropping a 4mm steel ball into a container of honey and measure the time it takes for the ball to pass between two marks as shown. If the time is 13 seconds, what is the honey's viscosity. Assume the density of the honey is 1450 kg/m3 and the density of the steel ball is 7800 kg/m³. Honey 5 cm

P2, µ2 2h P1 Po ρ1, μι L Figure 3: Two layer flow for (b) (b) Consider two immiscible (do not mix) fluid layers with different densities and viscosities which glide smoothly between two parallel horizontal walls, as shown in figure 3. Let pı and p2 be the densities and µ1 and µ2 be the viscosities of the two fluids, respectively. The flow is the result of an imposed constant pressure gradient, 2, similar to that of the Poiseuille flow. Assume a steady, incompressible, parallel viscous flow with p1 > P2 and µi > µ2- (i) Using the Navier-Stokes equations find the velocity profiles of both fluids. (ii) Ensure the fluid obeys the following conditions: The shear stress is continuous at the interface between the two fluids. • The velocity profile is continuous at the interface between the two fluids. No-slip boundary at the walls. (iii) Sketch the velocity profile. (iv) Determine where the maximum velocity occurs and explain why. (Hint: think about the respective viscosities and densities).…

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