HW_Week1 - 32 Chapter 1 E Introduction Section 1.4 Measures...

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Unformatted text preview: 32 Chapter 1 E Introduction . Section 1.4 Measures of Fluid Mass and Weight 1.22 Obtain a photographfimage of a situation in which the den- sity or specific weight of a fluid is important. Print this photo and write a brief paragraph that describes the situation involved. 1.23 A tank contains 500 kg of a liquid whose specific gravity is 2. Determine the volume of the liquid in the tank. 1.24 Clouds can weigh thousands of pounds due to their liquid water content. Often this content is measured in grams per cubic meter (glma). Assume that a cumulus cloud occupies a volume of one cubic kilometer, and its liquid water content is 0.2 glm3. (a) What is the volume of this cloud in cubic miles? (b) How much does the water in the cloud weigh in pounds? 1.25 A tank of oil has a mass of 25 slugs. (a) Determine its weight in pounds and in newtons at the earth’s surface. (b) What would be its mass (in slugs) and its weight (in pounds) if located on the moon’s surface where the gravitational attraction is approximately one«sixth that at the earth’s surface? 1.26 A certain object weighs 300 N at the earth’s surface. Deter— mine the mass of the object (in kilograms) and its weight (in new- tons) when located on a planet with an acceleration of gravity equal to 4.0 ft/sz. 1.27 The density of a certain type of jet fuel is 775 kglma. De— termine its specific gravity and specific weight. 1.23 A hydrometer is used to measure the specific gravity of liq- uids. (See Video V2.8.) For a certain liquid, a hydrometer read- ing indicates a specific gravity of 1.15. What is the liquids den- sity and specific weight? Express your answer in SI units. 1.29 An open, rigid—walled, cylindrical tank contains 4 ft3 of wa- ter at 40 °F. Over a 24nhour period of time the water temperature varies from 40 to 90 °F. Make use of the data in Appendix B to determine how much the volume of water will change. For a tank diameter of 2 ft, would the corresponding change in water depth be very noticeable? Explain. T130 Estimate the number of pounds of mercury it would take to fill your bathtub. List all assumptions and show all calculations. 1.31 A mountain clirnber’s oxygen tank contains 1 lb of oxygen when he begins his trip at sea level where the acceleration of grav- ity is 32.174 fb'sz. What is the weight of the oxygen in the tank when he reaches the top of Mt. Everest where the acceleration of gravity is 32.082 ftr'SQ? Assume that no oxygen has been removed from the tank; it will be used on the descent portion of the climb. 1.32 The information on a can of pop indicates that the can con- tains 355 mL. The mass of a full can of pop is 0.369 kg while an empty can weighs 0.153 N. Determine the specific weight, den— sity, and specific gravity of the pop and compare your results with the corresponding values for water at 20 °C. Express your results in SI units. *133 The variation in the density of water, ,0, with temperature, T, in the range 20 °C S T S 50 °C, is given in the following table. Density (kg/m3) 1998.2“ 997.1 995.7 994.1 9922‘. 9902* 988.1 20 25 30 35 40 45 50 Temperature (“(3) Use these data to determine an empirical equation of the form p = c; + all” + cfl‘z which can be used to predict the density over the range indicated. Compare the predicted values with the data given. What is the density of water at 42.1 °C? 1.34 If I cup of cream having a density of 1005 kgjrn3 is turned into 3 cups of whipped cream, determine the specific gravity and specific weight of the whipped cream. i135 The presence of raindrops in the air during a heavy rain'« storm increases the average density of the air—water mixture. Esti— mate by what percent the average air—water density is greater than that of just still air. State all assumptions and show calculations. Section 1.5 Ideal Gas Law 1.36 Determine the mass of air in a 2 m3 tank if the air is at room temperature, 20 °C, and the absolute pressure within the tank is 200 kPa (abs). 1.37 Nitrogen is compressed to a density of 4 kglm3 under an ab— solute pressure of 400 ltPa. Determine the temperature in degrees Celsius. 1.38 The temperature and pressure at the surface of Mars during a Martian spring day were determined to be —50 “C and 900 Pa, respectively. (a) Determine the density of the Martian atmosphere for these conditions if the gas constant for the Martian atmosphere is assumed to be equivalent to that of carbon dioxide. (13) Compare the answer from part (a) with the density of the earth’s atmosphere during a spring day when the temperature is 18 °C and the pres- sure 101.6 kPa (abs). 1.39 A closed tank having a volume of 2 ft3 is filled with 0.30 lb of a gas. A pressure gage attached to the tank reads 12 psi when the gas temperature is 80 °F. There is some question as to whether the gas in the tank is oxygen or helium. Which do you think it is? Explain how you arrived at your answer. 1.40 A compressed air tank contains 5 kg of air at a temperature of 80 “C. A gage on the tank reads 300 kPa. Determine the vol- ume of the tank. 1.41 A rigid tank contains air at a pressure of 90 psia and a tem- perature of 60 °F. By how much will the pressure increase as the temperature is increased to 110 ”F? 1.42 The helium~filled blimp shown in Fig. P142 is used at var- ious athletic events. Determine the number of pounds of helium within it if its volume is 68,000 ft3 and the temperature and pres— sure are 80 °F and 14.2 psia, respectively. EFIGURE P1.42 *1.43 Develop a computer program for calculating the density of an ideal gas when the gas pressure in pascals (abs), the tem— perature in degrees Celsius, and the gas constant in J/kg - K are specified. Plot the density of helium as a function of temperature from 0 °C to 200 °C and pressures of 50, 100, 150, and 200 kPa (abs). Section 1.6 Viscosity (Also see Lab Problems 1.104 and 1.105.) 1.44 Obtain a photographfimage of a situation in which the vis- cosity of a fluid is important. Print this photo and write a brief paragraph that describes the situation involved. 1.45 For flowing water, what is the magnitude of the velocity gra- dient needed to produce a shear stress of 1.0 Nlmz? 1.46 Make use of the data in Appendix B to determine the dy- namic viscosity of glycerin at 85 °F. Express your answer in both SI and BG units. 1.47 One type of capillary-tube viscometer is shown in Video V1.5 and in Fig. P1.47. For this device the liquid to be tested is drawn into the tube to a level above the top etched line. The time is then obtained for the liquid to drain to the bottom etched line. The kinematic viscosity, v, in 1112/8 is then obtained from the equa- tion I» = 101‘! where K is a constant, R is the radius of the capil- lary tube in mm, and t is the drain time in seconds. When glyc— erin at 20 °C is used as a calibration fluid in a particular viscometer, the drain time is 1430 3. When a liquid having a density of 970 kgim3 is tested in the same viscometer the drain time is 900 5. What is the dynamic viscosity of this. liquid? Glass strengthening 3 bridge I ll.) Etched lines Capillary tube \ IFIGURE P1.47 1.48 The viscosity of a soft drink was determined by using a cap illary tube viscometer similar to that shown in Fig. P1.47 and Video VLS. For this device the kinematic viscosity, 1:, is directly propor- tional to the time, t, that it takes for a given amount of liquid to flow through a small capillary tube. That is, v = Kr. The following data were obtained from regular pop and diet pop. The corre- sponding measured specific gravities are also given. Based on these data, by what percent is the absolute viscosity, n, of regular pop greater than that of diet pop? ' Regular pop Diet pop 1(8) 377.8 300.3 SG 1.044 1.003 ‘ 1.49 Determine the ratio of the dynamic viscosity of water to air at a temperature of 60 °C. Compare this value with the corresponding ratio of kinematic viscositics. Assume the air is at standard atmos- pheric pressure. _1.50 The viscosity of a certain fluid is 5 X 10—4 poise. Detemtine its viscosity in both SI and BG units. 1.51 The kinematic viscosity of oxygen at 20 °C and a pressure Of 150 era (abs) is 0.104 stokes. Determine the dynamic viscosity 0f oxygen at this temperature and pressure. *1-52 Fluids for which the shearing stress; 7, is not linearly related to the rate of shearing strain, 11, are designated as non— Newtonian fluids. Such fluids are commonplace and can exhibit unusual behavior, as shown in Video V1.6. Some experimental data :btained for a particular non—Newtonian fluid at 80 °F are shown elow. Problems 33 Tail/112) 0 l 2.11 7.32 i 18.5 31.7 1: (set) a so 100 150 200 Plot these data and fit a second-order polynomial to the data using a suitable graphing program. What is the apparent viscosity of this fluid when the rate of shearing strain is 70 3‘]? Is this apparent vis- cosity larger or smaller than that for water at the same tempera- ture? 1.53 Water flows near a flat surface and some measurements of the water velocity, u, parallel to the surface, at different heights, y, above the surface are obtained. At the surface y = 0. After an analysis of the data, the lab technician reports that the velocity distribution in the range 0 < y < 0.1 ft is given by the equation :1 : (181+ any + 4.1 x 105:3 with u in his when y is in ft. (a) Do you think that this equation would be valid in any system of units? Explain. (b) Do you think this equation is correct? Explain. You may want to look at Video 1.4 to help you arrive at your answer. 1.54 Calculate the Reynolds numbers for the flow of water and for air through a 4-nun»diameter tube, if the mean velocity is 3 m/s and the temperature is 30 °C in both cases (see Example 1.4). As- sume the air is at standard atmospheric pressure. 1.55 For air at standard atmospheric pressure the values of the constants that appear in the Sutherland equation (Eq. 1.10) are C = 1.458 x 1ortkg/(m - s - Km) and s = 110.4 K. Use these values to predict the viscosity of air at 10 °C and 90 °C and com— pare with values given in Table 13.4 in Appendix B. >I1.56 Use the values of viscosity of air given in Table 8.4 at tem- peratures of 0, 20, 40, 60, 80, and 100 °C to determine the con- stants C and S which appear in the Sutherland equation (Eq. 1.10). Compare your results with the values given in Problem 1.55. (Hint: Rewrite the equation in the form [1. and plot I‘m/u versus T. From the slope and intercept of this curve, C and S can be obtained.) 1.57 The viscosity of a fluid plays a very important role in deter— mining how a fluid flows. (See Video V1.3.) The value of the vis- cosity depends not only on the specific fluid but also on the fluid temperature. Some experiments show that when a liquid, under the ' action of a constant driving pressure, is forced with a low veloc— ity, V, through a small horizontal tube, the velocity is given by the equation V = K/u. in this equation K is a constant for a given tube and pressure, and ,u. is the dynamic viscosity. For a particular liq— uid of interest, the viscosity is given by Andrade’s equation (Eq. 1.11) withD = 5 x 10—7Ib's/fi2 andB = 4000 °R. By what per- centage will the velocity increase as the liquid temperature is in— creased from 40 °F to 100 °F? Assume all other factors remain con— stant. >31.58 Use the value of the viscosity of water given in Table B.2 at temperatures of 0, 20, 40, 60, 80, and 100 °C to determine the constants D and B which appear-in Andrade’s equation (Eq. 1.11). Calculate the value of the viscosity at 50 °C and compare with the value given in Table 13.2. (Hint: Rewrite the equation in the form 1 lnu=(B)}+lnD and plot In 11. versus 1/T. From the slope and intercept of this curve, B and D can be obtained. If a nonlinear curve-fitting program is 34 Chapter 1 E Introduction available the constants can be obtained directly from Eq. 1.11 with— out rewriting the equation.) 1.59 For a parallel plate arrangement of the type shown in Fig. 1.5 it is found that when the distance between plates is 2 mm, a shearing stress of 150 Pa develops at the upper plate when it is puiled at a velocity of 1 mls. Determine the viscosity of the fluid between the plates. Express your answer in SI units. 1.60 Two flat plates are oriented parallel above a fixed lower plate as shown in Fig. P1.60. The top plate, located a distance b above the fixed plate, is pulled along with speed V. The other thin plate is located a distance cb, where 0 < c < 1, above the fixed plate. This plate moves with speed V“ which is determined by the vis- cous shear forces imposed on it by the fluids on its top and bot- tom. The fluid on the top is twice as viscous as that on the bot— tom. Plot the ratio VIIV as a function of c for 0 < c < 1. finger w—m a 'L , EFIGUFIE P1.60 1.61 There are many fluids that exhibit non-Newtonian behavior (see, for example, Video V1.6). For a given fluid the distinction between Newtonian and non-Newtonian behavior is usually based on measurements of shear stress and rate of shearing strain. As- sume that the viscosity of blood is to be determined by measure- ments of shear stress, 7, and rate of shearing strain, du/dy, ob- tained from a small blood sample tested in a suitable viscometer. Based on the data given below determine if the blood is a New- tonian or non—Newtonian fluid. Explain how you arrived at your answer. 7(Nlm2) 0.04 1 0.06 0.12 l0.l8 l 0.30 0.52 I 1.12 +3.10 daddy (5-1) 2.25 4.50 11.25 22.5 45.0 90.0 225 450 1.62 The sled shown in Fig. P1.62 slides along on a thin horizontal layer of water between the ice and the runners. The horizontal force that the water puts on the runners is equal to 1.2 lb when the sled’s speed is 50 st. The total area of both runners in contact with the wa— ter is 0.03 at, and the viscosity of the water is 3.5 x 10—51mm? Determine the thickness of the water layer under the runners. Assume a linear velocity distribution in the water layer. ”FIGURE 131.62 1.63 A 25-mmvdiameter shaft is pulled through a cylindrical bear- ing as shown in Fig. P163. The lubricant that fills the 03-min gap between the shaft and bearing is an oil having a kine« matic viscosity of 8.0 X 10—4 mz/s and a specific gravity of 0.91. Determine the force P required to pull the shaft at a velocity of 3 mls. Assume the velocity distribution in the gap is linear. Bearing HEW—1m Lubricant «———th.5m——-I IFIGUFIE P1163 1.64 A 10-kg block slides down a smooth inclined surface as shown in Fig. P164. Determine the terminal velocity of the block if the 0.1-mm gap between the block and the surface con- tains SAE 30 oil at 60 ”F. Assume the velocity distribution in the gap is linear, and the area of the block in contact with the oil is 0.1 m2. EFIGUFIE P1.64 1.65 A layer of water flows down an inclined fixed surface with the velocity profile shown in Fig. Pl.65. Determine the magnitude and direction of the shearing stress that the water exerts on the fixed surface for U = 2 m/s and h = 0.1 m. FIGURE P155 $1.66 Standard air flows pasta flat surface and velocity measure- ments near the surface indicate the following distribution: y(ft) 40.005 0.01 P02 0.04 l 0.06 i 0.03 u(ft/s) 0.74 _ 1.51 3.03 6.37 10.21 14.437 The coordinate y is measured normal to the surface and u is the velocity parallel to the surface. {3) Assume the velocity distribu- tion is of the form U : Cry + C2}’3 and use a standard curve-fitting technique to determine the constants C, and C2. (b) Make use of the results of part (a) to determine the magnitude of the shearing stress at the wall (y = 0) and at y x 0.05 ft. 1.67 A new computer drive is proposed to have a disc, as shown in Fig. Pl.67. The disc is to rotate at 10,000 rpm, and the reader head is to be positioned 0.0005 in. 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. Stationary reader head 024“ die Rotating disc HFIGURE P1.67 1.68 The space between two 6~in.-long concentric cylinders is filled with glycerin (viscosity 2 8.5 X 10‘3 lb - s/ftz). The inner cylinder has a radius of 3 in. and the gap width between cylinders is 0.1 in. Determine the torque and the power required to rotate the inner cylinder at 180 rev/min. The outer cylinder is fixed. As- sume the velocity distribution in the gap to be linear. 1.69 A pivot bearing used on the shaft of an electrical instrument is shown in Fig. P1.69. An oil with a viseosity of ,u. = 0.0101b-slft2 fills the 0.001-in. gap between the rotating shaft and the station- ary base. Determine the frictional torque on the shaft when it re- tates at 5,000 rpm. 1 Q4) 5,000 rpm 0.2m. EFIGUFIE P1.69 1.70 The viscosity of liquids can be measured through the use of a rotating cylinder viscometer of the type illustrated in Fig. PI.70. In this device the outer cylinder is fixed and the inner cylinder is rotated With an angular velocity, to. The torque 37' required to develop to is measured and the viscosity is calculated from these two measurements. (a) Develop an equation relating [.L, (0, g, 8, R0, and R... Neglect and effects and assume the velocity distribution in the gap is lin- Ear. (b) The following torque—angular velocity data were obtained with a rotating Cylinder viscometer of the type discussed in part (a). Torque(ft-lb) 13.1 26.0 39.5 '52.? 64.9 78.6 Angular veloeity (rad/s) 1.0 2.0 3.0 4.0 5.0 6.0 Problems 35 For this viscometer R0 = 2.50 in., Rf = 2.45 in., and t’ = 5.00 in. Make use of these data and a standard curve-fitting program to de— termine the viscosity of the liquid contained in the viscometer. Fixed outer cylinder EFIGURE P1.70 1.71 A l2-in.-diameter circular plate is placed over a fixed bot— tom plate with a 0. l~in. gap between the two plates filled with glyc~ erin as shown in Fig. P1.7l. Determine the torque required to ro~ tate the circular plate slowly at 2 rpm. Assume that the velocity distribution in the gap is linear and that the shear stress on the edge of the rotating plate is negligible. Rotating plate E Torque/ EFIGURE P1.71 "ll-72 Vehicle shock absorbers damp out oscillations caused by road roughness. Describe how a temperature change may affect the operation of a shock absorber. 1.73 Some measurements on a blood sample at 37 °C (98.6 °F) indicate a shearing stress of 0.52 N/m2 for a corresponding rate of shearing strain of 200 3". Determine the apparent viscosity of the blood and compare it with the viscosity of water at the same temperature. Section 1.7 Compressibility of Fluids 1.74 Obtain a photograph/image of a situation in which the com- pressibility of a fluid is important. Print this photo and write a brief paragraph that describes the situation involved. 1.75 A sound wave is observed to travel through a liquid with a speed of 1500 m/s. The specific gravity of the liquid is 1.5. De- termine the bulk modulus for this fluid. 1.76 Estimate the increase in pressure (in psi) required to decrease a unit volume of mercury by 0.1%. 1.77 A l-m3 volume of water is contained in a rigid container. Es- timate the change in the volume of the water when a piston applies a pressure of 35 MP3. 1.78 Determine the speed of sound at 20 °C in (a) air, (13) helium, and (c) natural gas (methane). Express your answer in We 1.79 Air is enclosed by a rigid cylinder containing a piston. A pressure gage attached to the cylinder indicates an initial reading of 25 psi. Determine the reading on the gage when the piston has compressed the air to one—third its original volume. Assume the manometer the air pressure is 16 psia. Determine the reading on the Pressure gage for a differential reading of 4 ft on the manometer. Express your answer in psi (gage). Assume standard atmospheric pressure and neglect the weight of the air columns in the manometer. 2.29 A closed cylindrical tank filled with water has a hemispherical dome and is connected to an inverted piping system as shown in Fig. P229. The liquid in the top part of the piping system has a specific gravity of 0.8, and the remaining parts of the system are filled with water. If the pressure gage reading and is ...
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