Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr.
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1 Reading Assignments Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr. Sert) Study Set 1 You can find the answers of some of the following questions in your textbook. For others you need to go to other references. R1. Knudsen number is a non-dimensional number defined as follows Kn = Mean free path Characteristic length What do mean free path and characteristic length mean? What is the mean free path of air under standard conditions? What is the relation between the Knudsen number and the continuum assumption? R2. Viscosity of liquids decrease with increasing temperature. Gases show an opposite behavior. Read the reason behind this in your textbook. R3. What is the use of Sutherland s and Andrade s equations? Read in your textbook. R4. Surface tension is a fluid property. Read the related section in your textbook. Watch the related Munson s book movies titled Floating razor blade, Capillary rise and Contact angle. You can find a link to these movies at the course web site R5. Vapor pressure is a fluid property. Read the related section in your textbook. Understand the relation between vapor pressure, boiling and cavitation. R6. Some materials are called viscoelastic. What does it mean? Find examples of viscoelastic materials. R7. What is rheology? R8. Viscosity values in Pa s are small. poise and more frequently centipoise (cp) are also used in the industry as units of viscosity. How much Pa s is 1 cp? Similarly, centistokes (cst) is used for kinematic viscosity. How much m 2 /s is 1 cst? R9. What is a capillary tube viscometer? Watch the Munson s book movie showing it in operation. R10. We use detergents for better cleaning of clothes. They include surfactants. What s their role as far as surface tension is concerned? How do they improve cleaning? 1. Provide 1 or 2 sentence definitions of the following terms Continuum assumption Fluid particle Mach number Modulus of elasticity Fluid Newton s law of viscosity Newtonian fluid Bingham plastic Surface tension Vapor pressure Cavitation 1
2 2. a) Express the dimensions of kinematic viscosity in terms of basic dimensions M, L and T. b) If V is the characteristic speed and L is the characteristic length in a flow problem, and ν is the kinematic viscosity of the flowing fluid, determine the non-dimensional parameter that can be obtained by combining these three. This is one of the most important non-dimensional numbers of fluid mechanics. Learn its name. 3. (Munson) In a test to determine the modulus of elasticity of a liquid, it was found that as the pressure is increased from 90 kpa to 15 MPa, the volume decreased from 148 cm 3 to cm 3. Determine the modulus of elasticity of this liquid. 4. Consider water at 15 o C and 1 atm pressure. Using the appendix of your textbook, determine the percent change in its a) density b) viscosity when its temperature is raised to 40 o C. 5. What is the relation between shear stress and angular deformation (shear strain) for solids? What about for fluids? 6. Wall paint and printing ink are manufactured to have shear thinning and shear thickening characteristics, respectively. Why is that so? 7. Find examples of Bingham plastic type fluids. 8. (Aksel) A square plat plate with a side length of 0.8 m and a weight of 50 N slides down an inclined surface. The oil film between the plate and the surface has a thickness of 1 mm. Viscosity of the oil is 0.6 Pa s. Neglecting the effects at the edges of the plate and the air drag acting on its top surface, find its terminal speed. Oil is Newtonian and the velocity profile across it is linear. 1
3 9. (Aksel) A thin plate is pulled at a constant velocity of U o through a narrow gap of height h. The upper side of the plate is filled with a fluid of viscosity μ, while the lower side is filled with another fluid of viscosity 2μ. Assuming that both fluids are of Newtonian type and velocity profiles are linear, calculate the distance l in terms of h so that the force required to pull the plate is minimum. Warning: Be careful about the signs and directions of stresses and forces. 10. (Munson) A computer drive has a disc rotating at 10,000 rpm. Reader head is to be positioned mm above the surface of the disc. Estimate the shearing force on the reader head as result of the air between the disc and the head. Velocity profile across the air is assumed to be linear. Hint: Shear stress on the reader head is not constant, and shear force calculation requires an integration. However, the area of the reader head is small, so as the variation of shear stress over it. Therefore, it is possible to consider an average shear stress to simplify the calculation without introducing significant error. Top view Side view Stationary reader head 5 mm diameter mm 50 mm Rotating disk 2
4 11. (Aksel) In some electric measuring devices, sudden rotations of the pointer mechanism is dampened by having a circular disc to turn with the pointer in a container of oil. For the disc shown below determine the damping torque. Oil is Newtonian with a viscosity of 0.01 Pa s. Velocity profile across the oil is linear. Neglect the end effects. 12. (Fox) A viscometer is built from a conical pointed shaft that turns in a conical bearing. The gap between shaft and bearing is filled with a sample of the test oil. Obtain an algebraic expression for the viscosity μ of the oil as a function of viscometer geometry (H, a, and θ), turning speed ω, and applied torque T. Assume a linear velocity profile across the fluid. 13. (Fox) A spherical thrust bearing is shown. The gap between the spherical member and the housing is of constant width h. Obtain and plot an algebraic expression for the non-dimensional torque, T/(2πωμR 4 /h) on the spherical member, as a function of angle α. Assume linear velocity variation in the small gap. 3
5 14. (Fox) A shock-free coupling for a low-power mechanical drive is to be made from a pair of concentric cylinders. The annular space between the cylinders is to be filled with fluid. The drive must transmit P = 10 W of power. Other dimensions and properties are as shown. Neglect end effects and assume a linear velocity profile in the small gap between the cylinders. a) Determine the viscosity of the fluid. b) Do a research to find suitable fluids with the calculated viscosity. 15. (Çengel) The clutch system shown below is used to transmit torque through a 2 mm thick oil film with μ = 0.38 Pa s between two identical 30 cm diameter disks. When the driving shaft rotates at a speed of 1450 rpm, the driven shaft is observed to rotate at 1398 rpm. Assuming a linear velocity profile for the oil film, determine the transmitted torque. 16. An experiment is conducted to measure the viscous behavior of blood. Based on the obtained shear stress τ and rate of shearing strain data, which is tabulated below, determine if the blood behaves as Newtonian or not? If not determine what kind of a non-newtonian behavior does blood have? τ [Pa] Shearing strain [s -1 ] (Elger) (First work on the reading assignment R4) One way to measure the surface tension of a liquid is to use a ring as shown (figure shows the cross sectional view of the ring). The ring has an outside diameter of 10 cm and an inside diameter of 9.5 cm. The mass of the ring is 10 g. The force required to pull the ring from the liquid is 0.16 N. What is the surface tension of the liquid in N/m? 4
6 18. (Munson) (First work on the reading assignment R5) Small droplets of carbon tetrachloride at 20 o C are formed with a spray nozzle. If the average diameter of the droplets is 200 μm, what is the difference in pressure between the inside and outside of the droplets? 19. (Munson) (First work on the reading assignment R5) When a fluid flows through a sharp bend, low pressure may develop in localized regions of the bend. Estimate the minimum pressure that can develop without causing cavitation if the fluid is a) water at 80 o C, b) water at 10 o C? 5
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