An object of density Pa, volume Va, and weight Wa is

Perform the following estimations without using a calculator. (a) Estimate the mass of water (kg) in an Olympic-size swimming pool. (h) A drinking glass is being filled from a pitcher. Estimate the mass flow rate of the water (g1s). (c) Twelve heavyweight boxers coincidentally get on the same elevator in Great Britain. Posted on the elevator wall is a sign that gives the maximum safe combined weight of the passengers, Wmax, in stones (1 stone = 14 Ibm = 6 kg). If you were one of the boxers, estimate the lowest value of Wmax for which you would feel comfortable remaining on the elevator. (d) An oil pipeline across Alaska is 4.5 ft in diameter and 800 miles long. How many barrels of oil are required to fill the pipeline? (e) Estimate the volume of your body (em}) in two different ways. (Show your work.) (f) A solid block is dropped into water and very slowly sinks to the bottom. Estimate its specific gravity.

Calculate densities in Ibm/ft} of the following substances: (a) a liquid with density of995 kglm}. Use (i) conversion factors from the table on the inside front cover and (ii) Equation 3.1-2. (h) a solid with a specific gravity of 5.7.

The specific gravity of gasoline is approximately 0.70. (a) Determine the mass (kg) of 50.0 liters of gasoline. (b) The mass flow rate of gasoline exiting a refinery tank is 1150 kg/min. Estimate the volumetric flow rate in liters/s. (c) Estimate the average mass flow rate (Ibm/min) delivered by a gasoline pump. (d) Gasoline and kerosene (specific gravity = 0.82) are blended to obtain a mixture with a specific gravity of 0.78. Calculate the volumetric ratio (volume of gasoline/volume of kerosene) of the two compounds in the mixture, assuming Vb1end = Vgasoline + Vkerosene

Assume the price of gasoline in France is approximately 5 French francs per liter and the exchange rate is 5.22 francs per U.S. dollar. How much would you pay, in dollars, for 50.0 kg of gasoline in Student France, assuming gasoline has a specific gravity of 0.70. What would the same quantity of gasoline Workbook cost in the United States at a rate of $1.20 per gallon?

Liquid benzene and liquid n-hexane are blended to form a stream flowing at a rate of 700 Ibm/h. An on-line densitometer (an instrument used to determine density) indicates that the stream has a density of 0.850 g/mL. Using specific gravities from Table Rl, estimate the mass and volumetric feed rates of the two hydrocarbons to the mixing vessel (in American engineering units). State at least two assumptions required to obtain the estimate from the recommended data.

At 25C, an aqueous solution containing 35.0 wt% H2S04has a specific gravity of 1.2563. A quantity of the 35% solution is needed that contains 195.5 kg of H2S04. (a) Calculate the required volume (L) of the solution using the given specific gravity. (b) Estimate the percentage error that would have resulted if pure-component specific gravities of H2S04 (SG = 1.8255) and water had been used for the calculation instead of the given specific gravity of the mixture.

A rectangular block of solid carbon (graphite) Iloats at the interface of two immiscible liquids. The bottom liquid is a relatively heavy lubricating oiL and the top liquid is water. Of the total block volume, 54.2% is immersed in the oil and the balance is in the water. In a separate experiment, an empty flask is weighed, 35.3 cmJ of the lubricating oil is poured into the flask, and the flask is reweighed. If the scale reading was 124.8 g in the first weighing, what would it be in the second weighing? (Suggestion: Recall Archimedes' principle, and do a force balance on the block.)

A rectangular block floats in pure water with 0.5 in. above the surface and 1.5 in. below the surface. When placed in an aqueous solution, the block of material floats with 1 in. below the surface. Estimate the specific gravities of the block and the solution. (Suggestion: Call the horizontal crosssectional area of the block A. A should cancel in your calculations.)

An object of density Pa, volume Va, and weight Wa is thrown from a rowboat floating on the surface of a small pond and sinks to the bottom. The weight of the rowboat without the jettisoned object is Wb. Before the object was thrown out, the depth of the pond was hp1 , and the bottom of the boat was a distance hb1 above the pond bottom. After the object sinks, the values of these quantities are hp2 and hb2 . The area of the pond is Ap ; that of the boat is Ab Ab may be assumed constant, so that the volume of water displaced by the boat is Ab(hp - hb ). (a) Derive an expression for the change in the pond depth (hp2 - hp1 ). Does the liquid level of the pond rise or fall, or is it indeterminate? (b) Derive an expression for the change in the height of the bottom of the boat above the bottom of the pond (hb2 - hb1 ). Does the boat rise or fall relative to the pond bottom, or is it indeterminate?

Limestone (calcium carbonate) particles are stored in 50-L bags. The void fraction of the particulate matter is 0.30 (liter of void space per liter of total volume) and the specific gravity of solid calcium carbonate is 2.93. (a) Estimate the bulk density of the bag contents (kg CaC03/1iter of total volume). (b) Estimate the weight (W) of the filled bags. State what you are neglecting in your estimate. (c) The contents of three bags are fed to a ball mill, a device something like a rotating clothes dryer containing steel balls. The tumbling action of the balls crushes the limestone particles and turns them into a powder. (See pp. 20-31 of Perry's Chemical Engineers' Handbook, 7th ed.) The limestone coming out of the mill is put back into SO-L bags. Would the limestone (i) just fill three bags, (ii) fall short of filling three bags, or (iii) fill more than three bags? Briefly explain your answer.

A useful measure of an individual's physical condition is the fraction of his or her body that consists of fat. This problem describes a simple technique for estimating this fraction by weighing the individual twice, once in air and once submerged in water. (a) A man has body mass mb = 122.5 kg. If he stands on a scale calibrated to read in newtons, what would the reading be? If he then stands on a scale while he is totally submerged in water at 30C (specific gravity = 0.996) and the scale reads 44.0 N, what is the volume of his body (liters)? (Hint: Recall from Archimedes' principle that the weight of a submerged object equals the weight in air minus the buoyant force on the object, which in turn equals the weight of water displaced by the object. Neglect the buoyant force of air.) What is his body density, Pb (kg/L)? (b) Suppose the body is divided into fat and nonfat components, and that Xf (kilograms of fat/kilograms of total body mass) is the fraction of the total body mass that is fat: Xf = Prove that 1 1 Pb Pnf Xf = 1 1 Pf Pnf where Pb, Pf, and Pnf are the average densities ofthe whole body, the fat component, and the nonfat component, respectively. [Suggestion: Start by labeling the masses (mf and mb) and volumes (Vf and Vb) of the fat component of the body and the whole body, and then write expressions for the three densities in terms of these quantities. Then eliminate volumes algebraically and obtain an expression for mf/mb in terms of the densities. 5 ] (c) If the average specific gravity of body fat is 0.9 and that of nonfat tissue is 1.1, what fraction of the man's body in part (a) consists of fat? (d) The body volume calculated in part (a) includes volumes occupied by gas in the digestive tract, sinuses, and lungs. The sum of the first two volumes is roughly 100 mL and the volume of the SIf you can't work out the proof, take the given formula as valid and proceed to the next part. Problems 67 lungs is roughly 1.2 liters. The mass of the gas is negligible. Use this information to improve your estimate of Xf

Aqueous solutions of the amino acid L-isoleucine (lie) are prepared by putting 100.0 grams of pure water into each of six flasks and adding different precisely weighed quantities of lie to each flask. The densities of the solutions at 50.0:: 0.05C are then measured with a precision densitometer, with the following results: r (g lIe/lOO g H2O) 0.0000 0.8821 I 1.7683 2.6412 3.4093 4.2064 i i p (g solution/cm 0.99580 I 3) 0.98803 0.98984 I 0.99148 0.99297 0.99439 I (a) Plot a calibration curve showing the mass ratio. r. as a function of solution density, p, and fit a straight line to the data to obtain an equation of the form r = ap + b. (b) The volumetric flow rate of an aqueous lie solution at a temperature of 50C is 150 Llh. The density of a sample of the stream is measured at 50C and found to be 0.9940 gJcm3 Use the calibration equation to estimate the mass flow rate of lie in the stream (kg De/h). (c) It has just been discovered that the thermocouple used to measure the stream temperature was poorly calibrated and the temperature was actually 47C. Would the lie mass flow rate calculated in part (b) be too high or too low? State any assumption you make and briefly explain your reasonmg.

Before a rotameter can be used to measure an unknown flow rate, a calibration curve of flow rate versus rotameter reading must be prepared. A calibration technique for liquids is illustrated below. A flow rate is set by adjusting the pump speed; the rotameter reading is recorded, and the effluent from the rotameter is collected in a graduated cylinder for a timed interval. The procedure is carried out twice for each of several pump settings. ROTAMETER VARIABLE SPEED PUMP Rotameter Collection Volume Reading Time (min) Collected (cm3 ) 2 1 297 2 1 301 4 1 454 G 4 1 448 6 0.5 300 6 0.5 298 STOPWATCH 8 0.5 371 8 0.5 377 GRADUATED 10 0.5 440 CYLINDER 10 0.5 453 (a) Assuming the liquid is water at 25C, draw a calibration curve of mass flow rate, m(kg/min), versus rotameter reading, R, and use it to estimate the mass flow rate of a water stream for which the rotameter reading is 5.3. (b) The mean difference between duplicates, D;, provides an estimate of the standard deviation of a single measurement, which was given the symbol Sx on p. 18 of Chapter 2: fi- - Sx = 2 D; = 0.8862D; Moreover, confidence limits on measured values can be estimated to a good approximation using the mean difference between duplicates. For example, if a single measurement of Y yields a value Ymeasured, then there is a 95% probability that the true value of Y falls within the 95% confidence limits (Ymeasured - 1.74D;) and (Ym

How many of the following are found in 15.0 kmol of benzene (C6H6 )? (a) kg C6H6 ; (b) mol C6H6 ; (c) lb-mole C6H6 ; (d) mol (g-atom) C; (e) mol H; (f) g C; (g) g H; (h) molecules of C6H6 .

Liquid toluene is flowing through a pipe at a rate of 175 m3/h. (a) What is the mass flow rate of this stream in kg/min? (b) What is the molar flow rate in molls? (c) In fact, the answer to part (a) is only an approximation that is almost certain to be slightly in error. What did you have to assume to obtain the answer?

A mixture of methanol and methyl acetate contains 15.0 wt% methanol. (a) Using a single dimensional equation, determine the g-moles of methanol in 200.0 kg of the mixture. (b) The flow rate of methyl acetate in the mixture is to be 100.0 lb-mole/h. What must the mixture flow rate be in lbm/h?

The feed to an ammonia synthesis reactor contains 25 mole% nitrogen and the balance hydrogen. The flow rate of the stream is 3000 kg/h. Calculate the rate of flow of nitrogen into the reactor in kg/h. (Suggestion: First calculate the average molecular weight of the mixture.

A suspension of calcium carbonate particles in water flows through a pipe. Your assignment is to determine both the flow rate and the composition of this slurry. You proceed to collect the stream in a graduated cylinder for 1.00 min; you then weigh the cylinder, evaporate the collected water, and reweigh the cylinder. The following results are obtained: Mass of empty cylinder: 65.0 g Mass of cylinder + collected slurry: 565 g Volume collected: 455 mL Mass of cylinder after evaporation: 215 g Calculate (a) the volumetric flow rate and mass flow rate of the suspension. (b) the density of the suspension. (c) the mass fraction of CaC03 in the suspension

A mixture is 10.0 mole% ethyl alcohol, 75.0 mole% ethyl acetate (C4Hg 0 2 ), and 15.0 mole% acetic acid. Calculate the mass fractions of each compound. What is the average molecular weight of the mixture? What would be the mass (kg) of a sample containing 25.0 kmol of ethyl acetate?

Certain solid substances, known as hydrated compounds. have well-defined molecular ratios of water to some otherspecies. which often is a salt. For example, calcium sulfate dihydrate (commonly known as gypsum, CaS04 . 2H2 0), has 2 moles of water per mole of calcium sulfate; alternatively, it may be said that 1 mole of gypsum consists of 1 mole of calcium sulfate and 2 moles of water. The water in such substances is called water of hydration. (More information about hydrated salts is given in Chapter 6.) Solid gypsum is formed in a crystallizer and leaves that unit as a slurry (a suspension of solid particles in a liquid) of solid gypsum particles suspended in an aqueous CaS04 solution. The slurry flows from the crystallizer to a filter in which the particles are collected as aftlter cake. The filter cake, which is 95.0 wt% solid gypsum and the remainder CaS04 solution, is fed to a dryer in which all water (including the water of hydration in the crystals) is driven off to yield anhydrous (waterfree) CaS04 as product. A flowchart and relevant process data are given below. Solids content of slurry leaving crystallizer: 0.35 kg CaS04 . 2H20/L slurry CaS04 content of slurry liquid: 0.209 g CaS04/100 g H20 Specific gravities: CaS04' 2H20(s), 2.32; liquid solutions. 1.05 (a) Briefly explain in your own words the functions of the three units (crystallizer, filter, and dryer). (b) Take a basis of one liter of solution leaving the crystallizer and calculate the mass (kg) and volume (L) of solid gypsum, the mass of CaS04 in the gypsum, and the mass of CaS04 in the liquid solution. (c) Calculate the percentage recovery of CaS04-that is, the percentage of the total CaS04 (precipitated plus dissolved) leaving the crystallizer recovered as solid anhydrous CaS04.

Things were going smoothly at the Breaux Bridge Drug Co. pilot plant during the midnight to 8 a.m. shift until Therese Lagniappe, the reactor operator, let the run instruction sheet get too close to the Coleman stove that was being used to heat water to prepare Lagniappe's bihourly cup of Community Coffee. What followed ended in a total loss of the run sheet, the coffee, and a substantial portion of the novel Lagniappe was writing. Remembering the less than enthusiastic reaction she got the last time she telephoned her supervisor in the middle of the night, Lagniappe decided to rely on her memory of the required flow-rate settings. The two liquids being fed to a stirred-tank reactor were circulostoic acid (CSA: MW = 75, SG = 0.90) and flubitol (FB: MW = 90, SG = 0.75). The product from the system was a popular over-the-counter drug that simultaneously cures high blood pressure and clumsiness. The molar ratio of the two feed streams had to be between 1.05 and 1.10 mol CSAfmol FB to keep the contents of the reactor from forming a solid plug. At the time of the accident, the flow rate of CSA was 45.8 Llmin. Lagniappe set the flow of flubitol to the value she thought had been in the run sheet: 55.2 Llmin. Was she right? If not, how would she have been likely to learn of her mistake? (Note: The reactor was stainless steel, so she could not see the contents.

A mixture of ethanol (ethyl alcohol) and water contains 60.0% water by mass. (a) Assuming volume additivity of the components, estimate the specific gravity of the mixture at 20e. What volume (in liters) of this mixture is required to provide 150 mol of ethanol? (b) Repeat part (a) with the additional information that the specific gravity of the mixture at 20C is 0.93518 (making it unnecessary to assume volume additivity). What percentage error results from the volume additivity assumption?

A mixture of methane and air is capable of being ignited only if the mole percent of methane is between 5% and 15%. A mixture containing 9.0 mole% methane in air flowing at a rate of700. kg/h is to be diluted with pure air to reduce the methane concentration to the lower flammability limit. Calculate the required flow rate of air in mol/h and the percent by mass of oxygen in the product gas. (Note: Air may be taken to consist of 21 mole% O2 and 79% N2 and to have an average molecular weight of 29.0.)

A liquid mixture is prepared by combining N different liquids with densities PI, P2, ... , Pv. The volume of component i added to the mixture is Vi and the mass fraction of this component in the mixture is Xi. The components are completely miscible. Determine which of the following two formulas should be used to estimate the density of the liquid mixture, {5, if the volume of the mixture equals the sum of the pure-component volumes.? N {5 = L XiPi (A) i=l = i Xi (B) P J=l Pi Determine whether (A) or (B) is the correct formula (show your proof), and then use the correct formula to estimate the density (g/cm3) of a liquid mixture containing 60.0 wt% acetone, 25.0 wt% acetic acid, and 15.0 wt% carbon tetrachloride

A gaseous mixture of CO, CO2 , CH4, and N2 is analyzed with a gas chromatograph (see 3.26). The output appears on a strip-chart recorder, as shown here. For each of the three species, the area under the peak is approximately proportional to the number of moles of the indicated substance in the sample. From other information, it is known that the molar ratio of methane (CH4 ) to nitrogen is 0.200. (a) What are the mole fractions of the four species in the gas? (b) What is the average molecular weight of the gas?

A gas chromatograph (GC) is a device used to separate the components of a sample of a gas or liquid mixture and to provide a measure of the amount of each component in the sample. The output from a chromatographic analysis typically takes the form of a series of peaks on a strip-chart recorder. (See the preceding problem.) Each peak corresponds to a specific component, and the area under the peak is proportional to the amount of that component in the sample [n;{mol) = kiAi , where Ai is the area of the peak corresponding to the ith species]. The proportionality constants (k;) are determined in separate calibration experiments in which known amounts of the components are injected into the GC sample port and the corresponding peak areas are measured. (a) Prepare a spreadsheet to calculate the composition of a mixture from a set of peak areas obtained from a chromatograph. The spreadsheet should appear as follows:

Biomass combustion-burning of forests, grasslands, agricultural wastes, and other biological matter-is recognized as a serious threat to the environment~ The table below shows the distribution of carbon-containing compounds released to the atmosphere worldwide from all combustion sources as well as the portion coming from biomass burning. Compound Metric Tons C, All Sources 8700 1100 380 Metric Tons C, % from Biomass 40 26 10 The numbers in the middle column reflect annual quantities of carbon released to the atmosphere in the indicated compound; for example, 8700 metric tons of carbon (8.7 X 106 kg C) was released in carbon dioxide. (a) Determine the combined annual release (in metric tons) of all three species resulting from biomass combustion and the average molecular weight of the combined gases. (b) Find a reference on atmospheric pollution and list the environmental hazards associated with CO and COz release. What other elements might be released in environmentally hazardous forms if biomass is burned?

A 5.00-wt% aqueous sulfuric acid solution (p = 1.03 g/mL) flows through a 45-m long pipe with a 6.0 em diameter at a rate of 87 L/min. (a) What is the molarity of sulfuric acid in the solution? (b) How long (in seconds) would it take to fill a 55-gallon drum, and how much sulfuric acid (Ibm) would the drum contain? (You should arrive at your answers with two dimensional equations.) (c) The mean velocity of a fluid in a pipe equals the volumetric flow rate divided by the crosssectional area normal to the direction of flow. Use this information to estimate how long (in seconds) it takes the solution to flow from the pipe inlet to the outlet.

A gas stream contains 18.0 mole% hexane and the remainder nitrogen. The stream flows to a condenser, where its temperature is reduced and some of the hexane is liquefied. The hexane mole fraction in the gas stream leaving the condenser is 0.0500. Liquid hexane condensate is recovered at a rate of 1.50 L/min. (a) What is the flow rate of the gas stream leaving the condenser in mol/min? (Hint: First calculate the molar flow rate of the condensate and note that the rates at which \(\mathrm{C}_{6} \mathrm{H}_{14}\) and \(\mathrm{N}_{2}\) enter the unit must equal the total rates at which they leave in the two exit streams.) (b) What percentage of the hexane entering the condenser is recovered as a liquid?

The little-known rare earth element nauseum (atomic weight = 172) has the interesting property of being completely insoluble in everything but 12-year-old bourbon. This curious fact was discovered in the laboratory of Professor Ludwig von Schlimazel, the eminent German chemist whose 8Chemical & Engineering News, 68, 4(March 26,1990). 72 Chapter 3 Processes and Process Variables invention of the bathtub ring won him the Nobel Prize. Having unsuccessfully tried to dissolve nauseum in 7642 different solvents over a la-year period, Schlimazel finally came to the 30 mL of Old Aardvark Bottled-in-Bond that was the only remaining liquid in his laboratory. Always willing to suffer personal loss in the name ofscience, Schlimazel calculated the amount of nauseum needed to make up a 0.03 molar solution, put the Aardvark bottle on the desk of his faithful technician Edgar P. Settera, weighed out the calculated amount of nauseum and put it next to the bottle, and then wrote the message that has become part of history: "Ed Settera. Add nauseum!" How many grams of nauseum did he weigh out? (Neglect the change in liquid volume resulting from the nauseum addition.)

The reaction A -> B is carried out in a laboratory reactor. According to a published article the concentration of A should vary with time as follows: CA = CAoexp(-kl) where CAO is the initial concentration of A in the reactor and k is a constant. (a) If CA and CAO are in lb-moles/ft3 and I is in minutes, what are the units of k? (b) The following data are taken for CA(t): I(min) 0.5 1.0 1.5 2.0 3.0 5.0 10.0 CA(Ib-mole/ft)) 1.02 0.84 0.69 0.56 0.38 0.17 0.02 Verify the proposed rate law graphically (first determine what plot should yield a straight line), and calculate CAo and k. (c) Convert the formula with the calculated constants included to an expression for the molarity of A in the reaction mixture in terms of I(seconds). Calculate the molarity at I = 200 s.

Perform the following pressure conversions, assuming when necessary that atmospheric pressure is 1 atm. Unless otherwise stated, the given pressures are absolute. (a) 2600 mm Hg to psi (b) 275ft H20 to kPa (c) 3.00 atm to N/cm2 (d) 280 cm Hg to dyne/m2 (e) 20 cm Hg of vacuum to atm (absolute) (f) 25.0 psig to mm Hg (gauge) (g) 25.0 psig to mm Hg (absolute) (h) 325 mm Hg to mm Hg gauge (i) 35.0 psi to cm of carbon tetrachloride

A storage tank containing oil (SG =0.92) is 10.0 meters high and 16.0 meters in diameter. The tank is closed, but the amount of oil it contains can be determined from the gauge pressure at the bottom. (a) A pressure gauge connected to the bottom of the tank was calibrated with the top of the tank open to the atmosphere. The calibration curve is a plot of height of oil, h(m), versus Pg"g,(kPa). Sketch the expected shape of this plot. What height of oil would lead to a gauge reading of 68 kPa? What would be the mass (kg) of oil in the tank corresponding to this height? (b) An operator observes that the pressure gauge reading is 68 kPa and notes the corresponding liquid height from the calibration curve. What he did not know was that the absolute pressure above the liquid surface in the tank was 115 kPa when he read the gauge. What is the actual height of the oil? (Assume atmospheric pressure is 101 kPa.)

A rectangular block of height L and horizontal cross-sectional area A floats at the interface between two immiscible liquids, as shown below. Fluid 1 p,(glem3) Fluid 2 piglem3) Block ",,(glem3) HEAD Equipment Encyclopedia reactors (a) Derive a formula for the block density, Ph, in terms of the fluid densities p, and Pl., the heights ho, hI, and h" and the cross-sectional area A. (It is not necessary that all of these variables appear in the final result.) (b) Force balances on the block can be calculated in two ways: (i) in terms of the weight of the block and the hydrostatic forces on the upper and lower block surfaces; and (ii) in terms of the weight of the block and the buoyant force on the block as expressed by Archimedes' principle. Prove that these two approaches are equivalent.

The viewing window in a diving suit has an area of roughly 65 cm'. If an attempt were made to maintain the pressure on the inside of the suit at 1 atm, what force (N and lb,) would the window have to withstand if the diver descended to a depth of 150 m. Take the specific gravity of the water to be 1.05

The great Boston molasses flood occurred on January 15, 1919. In it, 2.3 million gallons of crude molasses flowed from a 30-foot high storage tank that ruptured, killing 21 people and injuring 150. The estimated specific gravity of crude molasses is 104. What were the mass of molasses in the tank in Ibm and the pressure at the bottom of the tank in Ib,/in.'? Give at least two possible causes of the tragedy.

The chemical reactor shown below has a cover (called a head) that is held in place by a series of bolts. The head is made of stainless steel (SG = 8.0), is 3 in. thick. has a diameter of 24 in.. and covers and seals an opening 20 in. in diameter. During turnaround, when the reactor is taken out of service for cleaning and repair, the head was removed by an operator who thought the reactor had been depressurized using a standard venting procedure. However, the pressure gauge had been damaged in an earlier process upset (the reactor pressure had exceeded the upper limit of the gauge), and instead of being depressurized completely, the vessel was under a gauge pressure of 30 psi.

In the movie The Drowning Pool, private detective Lew Harper (played by Paul Newman) is trapped by the bad guy in a room containing a swimming pool. The room may be considered rectangular, 5 meters wide by 15 meters long, with an open skylight window 10 meters above the floor. There is a single entry to the room. reached by a stairway: a locked 2-m high by 1-m wide door. whose bottom is 1 meter above the floor. Harper knows that his enemy will return in eight hours and decides he can escape by filling the room with water and floating up to the skylight. He plugs the drain with his clothes, turns on the water valves, and prepares to put his plan into action. (a) Prove that if the door is completely under water and h is the distance from the top of the door to the surface of the water, then the net force exerted on the door satisfies the inequality Encyclopedia Equipment manometer Encyclopedia Equipment manometer F > PH2oghAdoor (Don't forget that a pressure is also exerted on the door by the outside air.) (b) Assume that water enters the room at about five times the rate at which it enters an average bathtub and that the door can withstand a maximum force of 4500 newtons (about 1000Ibf ). Estimate (i) whether the door will break before the room fills and (ii) whether Harper has time to escape if the door holds. State any assumptions you make.

A housing development is served by a water tower with the water level maintained between 20 and 30 meters above the ground, depending on demand and water availability. Responding to a resident's complaint about the low flow rate of water at his kitchen sink, a representative of the developer came and measured the water pressure at the tap above the kitchen sink and at the junction between the water main (a pipe connected to the bottom of the water tower) and the feed pipe to the house. The junction is 5 m below the level of the kitchen tap. All water valves in the house were turned off. (a) If the water level in the tower was 25 m above tap level, what should be the gauge pressures (kPa) at the tap and junction? (b) Suppose the pressure measurement at the tap was lower than your estimate in part (a), but the measurement at the junction was as predicted. State a possible explanation. (c) If pressure measurements corresponded to the predictions in part (a), what else could be responsible for the low water flow to the sink?

Two mercury manometers, one open-end and the other sealed-end, are attached to an air duct. The reading on the open-end manometer is 25 mm and that on the sealed-end manometer is 800 mm. Determine the absolute pressure in the duct, the gauge pressure in the duct, and the atmospheric pressure, all in mm Hg.

Three different liquids are used in the manometer shown here. PI Pz T PA + Pe hz --L Pc (a) Derive an expression for PI - Pz in terms of PA, PB, Pc, hI, and hz (b) Suppose fluid A is methanol, B is water, and C is a manometer fluid with a specific gravity of 1.37; pressure Pz = 121.0 kPa; hI = 30.0 cm; and hz = 24.0 cm. Calculate PI (kPa)

The level of toluene (a flammable hydrocarbon) in a storage tank may fluctuate between 10 and 400 cm from the top of the tank. Since it is impossible to see inside the tank, an open-end manometer Student with water or mercury as the manometer fluid is to be used to determine the toluene level. One leg Workbook Problems 75 of the manometer is attached to the tank 500 cm from the top. A nitrogen blanket at atmospheric pressure is maintained over the tank contents. To atmosphere N2 t l It r----' t 10 em < h < 400 em Manometer fluid (H 20 or Hg) (a) When the toluene level in the tank is 150 cm below the top (h = 150 cm), the manometer fluid level in the open arm is at the height of the point where the manometer connects to the tank. What manometer reading, R (cm), would be observed if the manometer fluid is (i) mercury, (ii) water? Which manometer fluid would you use, and why? (b) Briefly describe how the system would work if the manometer were simply filled with toluene. Give several advantages of using the fluid you chose in part (a) over using toluene. (c) What is the purpose of the nitrogen blanket?

A fluid of unknown density is used in two manometers--one sealed-end, the other across an orifice in a water pipeline. The readings shown here are obtained on a day when barometric pressure is 756mmHg. Encyclopedia Equipment manometer 3.43 Palm P= 0 7.23 Tm 1 H---.L,...-- 20----- -_........... _- (a) (b) T 26 em 1- Encyclopedia Equipment manometer 3.44. What is the pressure drop (mm Hg) from point (a) to point (b)?

An open-end mercury manometer is connected to a low-pressure pipeline that supplies a gas to a laboratory. Because paint was spilled on the arm connected to the line during a laboratory renovation, it is impossible to see the level of the manometer fluid in this arm. During a period when the gas supply is connected to the line but there is no gas flow, a Bourdon gauge connected to the line downstream from the manometer gives a reading of 7.5 psig. The level of mercury in the open arm is 900 mm above the lowest part of the manometer.

An inclined manometer is a useful device for measuring small pressure differences. The formula given in Section 3.4 for the pressure difference in terms of the liquid-level difference h remains valid, but while h would be small and difficult to read for a small pressure drop if the manometer were vertical, L can be made quite large for the same pressure drop by making the angle of the inclination, e, small. (a) Derive a formula for h in terms of Land e. (b) Suppose the manometer fluid is water, the process fluid is a gas, the inclination of the manometer is e = 15, and a reading L = 8.7 cm is obtained. What is the pressure difference between points CDand@?

An open-end mercury manometer is to be used to measure the pressure in an apparatus containing a vapor that reacts with mercury. A 10 cm layer of silicon oil (SG = 0.92) is placed on top of the mercury in the arm attached to the apparatus. Atmospheric pressure is 765 mm Hg. (a) If the level of mercury in the open end is 365 mm below the mercury level in the other arm, what is the pressure (mm Hg) in the apparatus? (b) When the instrumentation specialist was deciding on a liquid to put in the manometer, she listed several properties the fluid should have and eventually selected silicon oil. What might the listed properties have been?

An orifice meter (see Figure 3.2-1) is to be calibrated for the measurement of the flow rate of a stream of liquid acetone. The differential manometer fluid has a specific gravity of 1.10. The calibration is accomplished by connecting the orifice meter in series with a rotameter that has previously been calibrated for acetone, adjusting a valve to set the flow rate, and recording the flow rate (determined from the rotameter reading and the rotameter calibration curve) and the differential manometer reading, h. The procedure is repeated for several valve settings to generate an orifice meter calibration curve of flow rate versus h. The following data are taken. (a) For each of the given readings, calculate the pressure drop across the orifice, \(\Delta\)P(mm Hg). (b) The flow rate through an orifice should be related to the pressure drop across the orifice by the formula \(\dot{V}=K(\Delta P)^{n}\) Verify graphically that the given orifice calibration data are correlated by this relationship, and determine the values of K and n that best fit the data. (c) Suppose the orifice meter is mounted in a process line containing acetone and a reading h = 23 mm is obtained. Determine the volumetric, mass, and molar flow rates of acetone in the line.

Convert the temperatures in parts (a) and (b) and temperature intervals in parts (c) and (d): (a) T = 85F to oR, C, K (b) T = -lOCtoK,oF,oR (c) t.T = 85C to K, of, oR (d) t.T = 1500R to of, DC, K

A temperature scale that never quite caught on was formulated by the Austrian chemist Johann Sebastian Farblunget. The reference points on this scale were OFB, the temperature below which Farblunget's postnasal drip began to bother him, and 1000FB, the boiling point of beer. Conversions between C and FB can be accomplished with the expression T("C) = 0.0940TCFB) + 4.00 Encyclopedia thermocouple Equipment Louis Louis. Farblunget's French nephew, attempted to follow in his uncle's footsteps by formulating his own temperature scale. He defined the degree Louie using as reference conditions the optimum serving temperature of marinated snails (1000 L corresponding to 1SC) and the temperature at which the elastic in his briefs began to relax (lOOooL corresponding to 43C). (a) At what temperature in of does beer boil? (b) What is the temperature interval of 10.0 Farblunget degrees equivalent to in DC, K, of, and OR? (c) Derive equations for T(C) in terms of T(OL) (see Example 3.5-1) and T(OL) in terms of TCFB). (d) What is the boiling point of ethane at 1 atm (Table B.1) in of, K, oR, FB, and L? (e) What is a temperature interval of SO.O Louie degrees equivalent to in Celsius degrees, Kelvin degrees, Fahrenheit degrees, Rankine degrees, and Farblunget degrees?

A thermocouple is a temperature-measurement device that consists of two dissimilar metal wires joined at one end. An oversimplified diagram follows. Metal 1 ~TENTIOMET, Metal 2 A voltage generated at the metal junction is read on a potentiometer or millivoltmeter. When certain metals are used, the voltage varies linearly with the temperature at the junction of the two metals: V(mV) = aTCC) + b An iron--constantan thermocouple (constantan is an alloy of copper and nickel) is calibrated by inserting its junction in boiling water and measuring a voltage V = 5.27 mY, and then inserting the junction in silver chloride at its melting point and measuring V = 24.88 mY. (a) Derive the linear equation for V (mV) in terms of T (0C). Then convert it to an equation for T in terms of V. (b) Ifthe thermocouple is mounted in a chemical reactor and the voltage is observed to go from 10.0 mV to 13.6 mV in 20 s, what is the average value of the rate of change of temperature. dT/ dr, during the measurement period?

A thermostat control with dial markings from 0 to 100 is used to regulate the temperature of an oil bath. A calibration plot on logarithmic coordinates of the temperature, T (OF), versus the dial Student setting, R, is a straight line that passes through the points (R1 = 20.0, T1 = lIO.OF) and (Rz = Workbook 40.0, Tz = 2S0.0F). 78 Chapter 3 Processes and Process Variables (a) Derive an equation for T CF) in terms of R. (b) Estimate the thermostat setting needed to obtain a temperature of 320F. (c) Suppose you set the thermostat to the value of R calculated in part (b) and the reading of a thermocouple mounted in the bath equilibrates at 295F instead of 320F. Suggest several possible explanations

As will be discussed in detail in Chapter 5, the ideal gas equation ofstate relates absolute pressure, P (atm); gas volume, V (liters); number of moles of gas, n(mol); and absolute temperature, T (K): PV = O.08206nT (a) Convert the equation to one relating P(psig), V(ft3), n(Ib-mole), and TCF). (b) A 30.0 mole% CO and 70.0 mole% N2 gas mixture is stored in a cylinder with a volume of 3.5 ft3 at a temperature of 85F. The reading on a Bourdon gauge attached to the cylinder is 500 psi. Calculate the total amount of gas (Ib-mole) and the mass of CO (Ibm) in the tank. (c) Approximately to what temperature CF) would the cylinder have to be heated to increase the gas pressure to 3000 psig, the rated safety limit of the cylinder? (The estimate would only be approximate because the ideal gas equation of state would not be accurate at pressures this high.)

Streams of methane and air (79 mole% N2 , the balance O2) are combined at the inlet of a combustion furnace preheater. The pressures of each stream are measured with open-end mercury manometers, the temperatures are measured with resistance thermometers, and the volumetric flow rates are measured with orifice meters. Measurement point 1 ! CH4 ---'--....... Air --...,t~--~ Measurement point 2 Measurement point 3 ,..-------, ! PREHEATER Data: Flowmeter 1: VI = 947 m3/h Flowmeter 2: V2 = 195 m3/min Manometer 1: hI = 232 mm Manometer 2: h2 = 156 mm Manometer 3: h3 = 74 mm Resistance thermometer 1: '1 = 26.159 ohms Resistance thermometer 2: '2 = 26.157 ohms Resistance thermometer 3: '3 = 44.789 ohms Atmospheric pressure: A sealed-end mercury manometer reads h = 29.76 in. The resistance thermometers were calibrated by measuring their resistances at the freezing and boiling points of water, with the following results: T = OC: , = 23.624 ohms T = 100C: , = 33.028 ohms A straight-line relationship between T and r may be assumed. The relationship between the total molar flow rate of a gas and its volumetric flow rate is, to a good approximation, given by a form of the ideal gas equation of state: 12.186P(atm)V(m3Is) T(K) where P is the absolute pressure of the gas. Problems 79 (a) Derive the resistance thermometer calibration formula for T(C) in terms of r(ohm). (b) Convert the given gas law expressions to an expression for h(kmol/min) in terms of P(mm Hg), T(C), and V(m3/min). (c) Calculate the temperatures and pressures at points 1,2, and 3. (d) Calculate the molar flow rate of the combined gas stream. (e) Calculate the reading of flowmeter 3 in m3/min. (f) Calculate the total mass flow rate and the mass fraction of the methane at point 3.

You are performing an experiment in which the concentration, CA, of a reactive species is measured as a function of time, t, at several temperatures, T. At a fixed temperature, CAvaries with t according to the relation (1) where CA(mol/liter) is the concentration of A at time t(min), CAo(mol/liter) is the inital concentration of A, and k[L/(mol'min)] is the reaction rate constant. The rate constant in turn depends on temperature, according to the formula k == koexp[-E/(8.314T)] (2) where ko is a contant, T (K) is the reactor temperature, and E (l/mol) is the reaction activation energy. Write a computer program that will carry out the following tasks: (a) Read in MA , the molecular weight of A, and NT, the number of temperatures at which measurements were made. (b) For the first temperature, read in the value of T in e, the number of data points, N; and the concentrations and times (t1. CAl), (t2, CAl)... , (tn, CAn), where the times are in minutes and the concentrations are in grams of Alliter. (c) Convert the temperature to kelvin and the concentrations to mol AIL. (d) Use the method of least squares (Appendix A.1) in conjunction with Equation 1 to find the value of k that best fits the data. (Hint: First cast the equation in the form y = kx + b.) Store the values of k and T in arrays. (e) Print out in a neat format the values of T (K), the converted concentrations (mol/L) and times. and k. (f) Repeat steps (b) through (d) for the other temperatures. [For extra credit: Use the method of least squares again in conjunction with Equation 2 to determine the value of E that best fits the calculated (T, k) values. Again, start by casting Equation 2 in the form y = ax +b.] It will be convenient to perform the least-squares slope calculation in a subroutine, since it must be done repeatedly. Test your program on the following data: MA = 65.0 glmol T = 94C T = 110C T = 127C T = 142C t(min) CA(glL) CA(g/L) CA(glL) CA(giL) 10 8.1 3.5 1.5 0.72 20 4.3 1.8 0.76 0.36 30 3.0 1.2 0.50 0.24 40 2.2 0.92 0.38 0.18 50 1.8 0.73 0.30 0.15 60 1.5 0.61 0.25 0.12