Problem 1: A cone-plate viscometer is a device used to measure a fluid's viscosity. The torque M required to turn a cone-plate viscometer depends on the angular velocity , the radius R, the cone angle and the viscosity of the test fluid μ: M = f(Q, R,0,μ) (it is assumed that inertial effect is negligible; thus the torque does not depend on the fluid's density). Make this torque relation dimensionless (note that the angle is dimensionless). 0 Ω 土 R 0 Fluid

question 3d

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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

Problem 6-1: The Reynolds number is an engineering parameter that relates to the volume flow rate of a fluid 4Q where vis πνd m² through a tube of diameter d as Red the fluid kinematic viscosity. Determine the Reynolds number and its uncertainty by general analysis given d = 50.4 ±0.1 mm, Q = 0.213 +0.005 S v = 0.999 × 10-6 ± 0.005 × 10-6 m². Which variable contributes the most to the overall uncertainty? Assume uncertainties are at 95 % confidence. S

(Dimensional Analysis) If the velocity V in a fluid flow depends on a dimension 1, the fluid density p, and the viscosity µ, show that this implies that the Reynolds number Vlp/µ is constant.

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).…

The kinematic viscosity of and specific gravity of a liquid are 3.5 x 10-4 m^2 /s and 0.79, respectively. What is the dynamic viscosity of the liquid in N-s/m^2?

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