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applied fluid mechanics

Questions and Answers of Applied Fluid Mechanics

An advertising sign for the ABC Paper Company is shown in Fig. 17.17. It is made from three flat disks, each with a diameter of 56.0 in. The disks are joined by 4.50-in-diameter tubes measuring 30 in
The four designs shown in Fig. 17.16 for the cross section of an emergency flasher lighting system for police vehicles are being evaluated. Each has a length of 60 in and a width of 9.00 in. Compare
A trapezoidal channel with a bottom width of 3.0 ft and side slopes having a ratio of 1:0.75 carries 0.80 ft3/s of water and is made from trowel-finished concrete. Use y = 0.05 ft in (d).
A triangular channel with side slopes having a ratio of 1:1.5 carries 0.68 ft3/s of water and is made from clean, excavated earth. Use y = 0.25 ft in (d).
For each section designed in Problem 14.36, compute the Froude number and tell whether the flow is subcritical or supercritical.Complete the following list of tasks for each of Problems
It is desired to carry 1.25 ft3/s of water at a velocity of 2.75 ft/s. Design the channel cross-section for each of the shapes shown in Table 14.3, which lists the most efficient sections for open
Repeat Problem 14.28, except that the channel is lined with smooth plastic sheets.Repeat ProblemFor the channel described in Problem 14.27, compute the normal discharge that would be expected for a
Determine the available NPSH for the pump in Practice Problem 7.14 if the water is at 80°F and the atmospheric pressure is 14.4 psia. Repeat the calculations for water at 180°F.
Oil with a specific gravity of 0.93 and a dynamic viscosity of 9.5 × 10-3 Pa∙s is flowing into the open tank shown in Fig. 11.23. The total length of 50 mm tubing is 30 m. For the 100 mm tubing
An orifice meter with a hole of $1 \mathrm{in}$. diameter is inserted into a $1 \frac{1 / 2}{2}$ in. sch 40 line carrying SAE 10 lube oil at $70^{\circ} \mathrm{F}(S G=0.93)$. A manometer using water
An orifice with a 3 in. diameter hole is mounted in a 4 in. diameter pipeline carrying water. A manometer containing an immiscible fluid with a specific gravity (SG) of 1.2 connected across the
An orifice with a 1 in. diameter hole is installed in a 2 in. sch 40 pipeline carrying SAE 10 lube oil at $100^{\circ} \mathrm{F}$. The pipe section where the orifice is installed is vertical, with
The flow rate in a $1.5 \mathrm{in}$. ID line can vary from 100 to $1000 \mathrm{bbl} /$ day, and you must install an orifice meter to measure it. If you use a differential pressure (DP) cell with a
A 4 in. sch 80 pipe carries water from a storage tank on top of a hill to a plant at the bottom of the hill. The pipe is inclined at an angle of $20^{\circ}$ to the horizontal. An orifice meter with
You must size an orifice meter to measure the flow rate of gasoline ( $\mathrm{SG}=0.72)$ in a $10 \mathrm{in}$. ID pipeline at $60^{\circ} \mathrm{F}$. The maximum flow rate expected is $1000
A 2 in. sch 40 pipe carries $\mathrm{SAE} 10$ lube oil at $100^{\circ} \mathrm{F}(\mathrm{SG}=0.928)$. The flow rate may be as high as $55 \mathrm{gpm}$, and you must select an orifice meter to
A 2 in. sch 40 pipe carries a $35^{\circ} \mathrm{API}$ distillate at $50^{\circ} \mathrm{F}(\mathrm{SG}=0.85)$. The flow rate is measured by an orifice meter, which has a diameter of $1.5
An orifice having a diameter of $1 \mathrm{in}$. is used to measure the flow rate of SAE 10 lube oil $(\mathrm{SG}=0.928)$ in a $2 \mathrm{in}$. sch 40 pipe at $70^{\circ} \mathrm{F}$. The pressure
An orifice meter is used to measure the flow rate of $\mathrm{CCl}_{4}$ in a $2 \mathrm{in}$. sch 40 pipe. The orifice diameter is 1.25 in., and a mercury ( $\mathrm{SG}=13.6)$ manometer attached to
An orifice meter is installed in a 6 in. ID pipeline that is inclined upward at an angle of $10^{\circ}$ from the horizontal. Benzene is flowing in the pipeline at the flow rate of $10 \mathrm{gpm}$.
You are to specify an orifice meter for measuring the flow rate of a $35^{\circ} \mathrm{API}$ distillate $(\mathrm{SG}=0.85$ ) flowing in a $2 \mathrm{in}$. sch 160 pipe at $70^{\circ} \mathrm{F}$.
You must select an orifice meter for measuring the flow rate of an organic liquid ( $\mathrm{SG}=0.8$, $\mu=15 \mathrm{cP}$ ) in a $4 \mathrm{in}$. sch 40 pipe. The maximum flow rate anticipated is
An oil with an $\mathrm{SG}$ of 0.9 and viscosity of $30 \mathrm{cP}$ is transported in a $12 \mathrm{in}$. $\mathrm{sch} .20$ pipeline at a maximum flow rate of $1000 \mathrm{gpm}$. What size
You want to use a venturi meter to measure the flow rate of water, up to $1000 \mathrm{gpm}$, through an 8 in. sch 40 pipeline. To measure the pressure drop in the venturi, you have a DP cell with a
Gasoline is pumped through a 2 in. sch 40 pipeline upward into an elevated storage tank at $60^{\circ} \mathrm{F}$. An orifice meter is mounted in a vertical section of the line, which uses a DP cell
You have been asked by your boss to select a flow meter to measure the flow rate of gasoline $(\mathrm{SG}=0.85)$ at $70^{\circ} \mathrm{F}$ in a 3 in. sch 40 pipeline. The maximum expected flow rate
A 2 in. sch 40 pipe is carrying water at a flow rate of $8 \mathrm{gpm}$. The flow rate is measured by means of an orifice with a $1.6 \mathrm{in}$. diameter hole. The pressure drop across the
The flow rate of $\mathrm{CO}_{2}$ in a $6 \mathrm{in}$. ID pipeline is measured by an orifice meter with a diameter of $5 \mathrm{in}$. The pressure upstream of the orifice is $10 \mathrm{psig}$,
An orifice meter is installed in a vertical section of a piping system, in which SAE 10 lube oil is flowing upward (at $100^{\circ} \mathrm{F}$ ). The pipe is $2 \mathrm{in}$. sch 40 , and the
You must install an orifice meter in a pipeline to measure the flow rate of $35.6^{\circ} \mathrm{API}$ crude oil at $80^{\circ} \mathrm{F}$. The pipeline diameter is $18 \mathrm{in}$. sch 40 , and
You are to specify an orifice meter for measuring the flow rate of a $35^{\circ} \mathrm{API}$ distillate $(\mathrm{SG}=0.85)$ flowing in a $2 \mathrm{in}$. sch 160 pipe at $70^{\circ} \mathrm{F}$.
A 6 in. sch 40 pipeline is designed to carry $\mathrm{SAE} 30$ lube oil at $80^{\circ} \mathrm{F}(\mathrm{SG}=0.87)$ at a maximum velocity of $10 \mathrm{ft} / \mathrm{s}$. You must install an
An orifice meter with a diameter of 3 in. is mounted in a 4 in. sch 40 pipeline carrying an oil with a viscosity of $30 \mathrm{cP}$ and an $\mathrm{SG}$ of 0.85 . A mercury manometer attached to the
A $35^{\circ} \mathrm{API}$ oil at $50^{\circ} \mathrm{F}$ is transported in a $2 \mathrm{in}$. sch 40 pipeline. The oil flow rate is measured by an orifice meter that is $1.5 \mathrm{in}$. in
A 6 in. sch 40 pipeline carries a petroleum fraction (viscosity $15 \mathrm{cP}, \mathrm{SG} 0.85$ ) at a velocity of $7.5 \mathrm{ft} / \mathrm{s}$, from a storage tank at $1 \mathrm{~atm}$ pressure
Water drains by gravity out of the bottom of a large tank, through a horizontal $1 \mathrm{~cm}$ ID tube, $5 \mathrm{~m}$ long that has a venturi meter mounted in the middle of the tube. The level in
Natural gas $\left(\mathrm{CH}_{4}\right)$ is flowing in a 6 in. sch 40 pipeline at 50 psig and $80^{\circ} \mathrm{F}$. A 3 in. diameter orifice is installed in the line, which reads a pressure drop
A solvent $(\mathrm{SG}=0.9, \mu=0.8 \mathrm{cP}$ ) is transferred from a storage tank to a process unit through a $3 \mathrm{in}$. sch 40 pipeline that is $2000 \mathrm{ft}$ long. The line contains
Rework Example 11.1 using the HDI method and tables for the properties of air, and compare the results with the example. Which answer do you think is the best, and why? (You should have access to a
An SRV must be sized to relieve hot water from a water heater at a rate of $20 \mathrm{lb}_{\mathrm{m}} / \mathrm{s}$. If the water is at $220^{\circ} \mathrm{F}$ and $45 \mathrm{psia}$, what nozzle
Air at $100 \mathrm{psia}$ and $60^{\circ} \mathrm{F}$ is being controlled through a venturi control valve. The backpressure at the valve discharge is $P_{2}=30 \mathrm{psia}$. The flow rate through
You want to control the flow rate of a liquid in a transfer line at $350 \mathrm{gpm}$. The pump in the line has the characteristics shown in Figure 8.2, with a 5 1/4 in. impeller. The line contains
A liquid with a viscosity of $25 \mathrm{cP}$ and an $\mathrm{SG}$ of 0.87 is pumped from an open tank to another tank in which the pressure is $15 \mathrm{psig}$. The line is $2 \mathrm{in}$. sch 40
Water at $60^{\circ} \mathrm{F}$ is to be transferred at a rate of $250 \mathrm{gpm}$ from the bottom of a storage tank to the bottom of a process vessel. The water level in the storage tank is $5
A piping system takes water at $60^{\circ} \mathrm{F}$ from a tank at atmospheric pressure to a plant vessel at 25 psig that is $30 \mathrm{ft}$ higher than the upstream tank. The transfer line
By careful streamlining, it is possible to reduce the drag coefficient of an automobile from 0.4 to 0.25 . How much power would this save at $40 \mathrm{mph}$ and $60 \mathrm{mph}$, assuming the
If your pickup truck has a drag coefficient equivalent to a $5 \mathrm{ft}$ diameter disk, and the same projected frontal area, how much horsepower is required to overcome wind drag at $40
You take a tumble while water skiing. The handle attached to the tow rope falls beneath the water and remains perpendicular to the direction of the boat's heading. If the handle is one inch in
Your new car is reported to have a drag coefficient of 0.3. If the cross-sectional area of the car is $20 \mathrm{ft}^{2}$, how much horsepower is used to overcome wind resistance at $40
The supports for a tall chimney must be designed to withstand a $120 \mathrm{mph}$ wind. If the chimney is $10 \mathrm{ft}$ in diameter and $40 \mathrm{ft} \mathrm{high}$, what is the wind force on
A speedboat is propelled by a water jet motor that takes water in at the bow through a $10 \mathrm{~cm}$ diameter duct and discharges it through a $50 \mathrm{~mm}$ diameter nozzle at a rate of $80
After blowing up a balloon, you release it without tying off the opening, and it flies out of your hand. If the diameter of the balloon is 6 in., the pressure inside it is $1 \mathrm{psig}$, and the
A mixture of titanium $(\mathrm{SG}=4.5)$ and silica $(\mathrm{SG}=2.65)$ particles, with diameters ranging from 50 to $300 \mu \mathrm{m}$, is dropped into a tank in which water is flowing upward.
A small sample of ground coal is introduced at the top of a column of water $30 \mathrm{~cm}$ high, and the time required for the particles to settle out is measured. If it takes $26 \mathrm{~s}$ for
You want to determine the viscosity of an oil which has an SG of 0.9. To do this, you drop a spherical glass bead $(\mathrm{SG}=2.7)$ with a diameter of $0.5 \mathrm{~mm}$ into a large vertical
A solid particle with a diameter of $5 \mathrm{~mm}$ and an $\mathrm{SG}$ of 1.5 is immersed in a liquid with a viscosity of $10 \mathrm{P}$ and an SG of 1 . How long will it take for the particle to
A hot air popcorn popper operates by blowing air through the popping chamber, which carries the popped corn up through a duct and out of the popper leaving the un-popped grains behind. The un-popped
You have a granular solid with $\mathrm{SG}=4$, which has particle sizes of $300 \mu \mathrm{m}$ and smaller. You want to separate out all of the particles with a diameter of $20 \mu \mathrm{m}$ and
You want to reproduce the experiment shown in the text which illustrates the wake behind a sphere falling in water at the point where the boundary layer undergoes transition from laminar to
You have a sample of crushed coal containing a range of particle sizes from 1 to $1000 \mu \mathrm{m}$ in diameter. You wish to separate the particles according to size by entrainment, in which they
A gravity settling chamber consists of a horizontal rectangular duct that is $6 \mathrm{~m}$ long, $3.6 \mathrm{~m}$ wide, and $3 \mathrm{~m}$ high. The chamber is used to trap sulfuric acid mist
A small sample of a coal slurry containing particles with equivalent spherical diameters from 1 to $500 \mu \mathrm{m}$ is introduced at the top of a water column $30 \mathrm{~cm}$ high. The
A slurry containing solid particles having a density of $2.4 \mathrm{~g} / \mathrm{cm}^{3}$, ranging in diameter from $0.001 \mathrm{in}$. to $0.1 \mathrm{in}$., is fed to a settling tank $10
A handful of sand and gravel is dropped into a tank of water $5 \mathrm{ft}$ deep. The time required for the solids to reach the bottom is measured and found to vary from 3 to $20 \mathrm{~s}$. If
It is desired to determine the size of pulverized coal particles by measuring the time it takes them to fall a given distance in a known fluid. It is found that the coal particles $(S G=1.35)$ take a
A water slurry containing coal particles $(S G=1.35)$ is pumped into the bottom of a large tank (10 ft diameter, $6 \mathrm{ft} \mathrm{high}$ ), at a rate of $500 \mathrm{gal} / \mathrm{h}$, and
In order to determine the settling characteristics of a sediment, you drop a sample of the material into a column of water. You measure the time it takes for the solids to fall a distance of $2
You want to separate all the coal particles having a diameter of 100 μm or larger from a slurry. To do this, the slurry is pumped into the bottom of a large tank. It flows upward and overflows over
A gravity settling chamber consists of a horizontal rectangular duct $6 \mathrm{~m}$ long, $3.6 \mathrm{~m}$ wide, $3 \mathrm{~m}$ high. The duct is used to trap sulfuric acid mist droplets entrained
Solid particles of diameter 0.1 mm and density 2 g/cm3 are to be separated from air in a horizontal settling chamber. If the air flow rate is 100 ft3/s and the maximum height of the chamber is 4 ft,
A settling tank contains solid particles that have a wide range of sizes. Water is pumped into the tank from the bottom and overflows on top at a rate of $10,000 \mathrm{gal} / \mathrm{h}$. If the
You want to use a viscous Newtonian fluid to transport small granite particles through a horizontal $1 \mathrm{in}$. ID $100 \mathrm{ft}$ long pipeline. The granite particles have a diameter of $1.5
An aqueous slurry containing particles with the size distribution shown in the following table is fed to a $20 \mathrm{ft}$ diameter settling tank (see, e.g., McCabe et al. (1993) or Perry's Handbook
A water stream contacts a bed of particles, which have diameters ranging from 1 to $1000 \mu \mathrm{m}$ and $S G=2.5$. The water stream flows upward at a rate of $3 \mathrm{~cm} / \mathrm{s}$. What
An aqueous slurry containing particles with $S G=4$ and a range of sizes up to $300 \mu \mathrm{m}$ flows upward through a small tube into a larger vertical chamber with a diameter of $10
A dilute aqueous $\mathrm{CaCO}_{3}$ slurry is pumped into the bottom of a classifier, at a rate of $0.4 \mathrm{~m}^{3} / \mathrm{s}$, and overflows at the top. The density of the solids is $2.71
A centrifuge that is $40 \mathrm{~cm}$ ID and $30 \mathrm{~cm}$ long has an overflow weir that is $5 \mathrm{~cm}$ wide. The centrifuge operates at a speed of $3600 \mathrm{rpm}$.(a) What is the
Solid particles with a diameter of $10 \mu \mathrm{m}$ and $S G=2.5$ are to be removed from an aqueous suspension in a centrifuge. The centrifuge inner radius is $1 \mathrm{ft}$, the outer radius is
A centrifuge is used to remove solid particles with a diameter of $5 \mu \mathrm{m}$ and $S G=1.25$ from a dilute aqueous stream. The centrifuge rotates at $1200 \mathrm{rpm}$ and is $3 \mathrm{ft}
A dilute aqueous slurry containing solids with a diameter of $20 \mu \mathrm{m}$ and $S G=1.5$ is fed to a centrifuge rotating at $3000 \mathrm{rpm}$. The radius of the centrifuge is $18
A centrifuge with a radius of $2 \mathrm{ft}$ and a length of $1 \mathrm{ft}$ has an overflow weir located $1 \mathrm{ft}$ from the centerline. If particles with $S G=2.5$ and diameters of $10 \mu
A centrifuge with a diameter of $20 \mathrm{in}$. operates at a speed of $1800 \mathrm{rpm}$. If there is a water layer 3 in. thick on the centrifuge wall, what is the pressure exerted on the wall?
A vertical centrifuge, operating at $100 \mathrm{rpm}$, contains an aqueous suspension of solid particles with $S G=1.3$ and radius of $1 \mathrm{~mm}$. When the particles are $10 \mathrm{~cm}$ from
You are required to design an aerocyclone to remove as much dust as possible from the exhaust coming from a rotary drier. The gas is air at $100^{\circ} \mathrm{C}, 1 \mathrm{~atm}$, and a rate of
An impurity in a water stream at a very small concentration is to be removed in a charcoal trickle bed filter. The filter is in a cylindrical column that is $2 \mathrm{ft}$ in diameter, and the bed
A trickle bed filter is composed of a packed bed of broken rock that has a shape such that the average ratio of the surface area to volume for the rock particles is $30 \mathrm{in} .^{-1}$ The bed is
A packed column that is $3 \mathrm{ft}$ in diameter with a packing height of $25 \mathrm{ft}$ is used to absorb an impurity from a methane gas stream using an amine solution absorbent. The gas flow
A packed column is used to scrub $\mathrm{SO}_{2}$ from air using water. The gas flow rate is $500 \mathrm{scfm} / \mathrm{ft}^{2}$ and the column operates at $90^{\circ} \mathrm{F}$ and $1
A stripping column packed with 2 in. metal Pall rings uses air at $5 \mathrm{psig}, 80^{\circ} \mathrm{C}$, to strip an impurity from an absorber oil $\left(S G=0.9\right.$, viscosity $=5
A packed column, which is $0.6 \mathrm{~m}$ in diameter and $4 \mathrm{~m}$ high containing $25 \mathrm{~mm}$ Raschig rings, is used in a gas absorption process to remove an impurity from the gas
A packed column is used to absorb $\mathrm{SO}_{2}$ from flue gas using an ethanol amine solution. The column is $4 \mathrm{ft}$ in diameter and has a packed height of $20 \mathrm{ft}$ and is packed
The amine solution has a specific gravity of 1.02 and a viscosity at the operating temperature of $1.5 \mathrm{cP}$. If the gas must leave the column at $25 \mathrm{psig}$ and a flow rate of $10,000
A packed absorption tower is used to remove $\mathrm{SO}_{2}$ from an air stream by absorption in a solvent. The tower is $5 \mathrm{ft}$. in diameter and $60 \mathrm{ft}$. high and contains 1.5 in.
A packed absorption column removes an impurity from a gas stream by contact with a liquid solvent. The column is $3 \mathrm{ft}$ in diameter and contains $25 \mathrm{ft}$ of No. 2 plastic Super
A fine aqueous suspension containing $1 \mathrm{lb}_{\mathrm{m}}$ of solids per $\mathrm{ft}^{3}$ of suspension is to be filtered in a constant pressure filter. It is desired to filter at an average
An aqueous slurry containing $1.5 \mathrm{lb}_{\mathrm{m}}$ of solid per gallon of liquid is pumped through a filter cloth by a centrifugal pump. If the pump provides a constant pressure drop of $150
A packed bed that consists of the same medium as that in Problem 3 is to be used to filter solids from an aqueous slurry. To determine the filter properties, you test a small section of the bed,
A slurry containing $1 \mathrm{lb}_{\mathrm{m}}$ of solids per gallon of water is to be filtered in a plate-and-frame filter having a total filtering area of $60 \mathrm{ft}^{2}$. The slurry is fed
A rotary drum filter that is $6 \mathrm{ft}$ in diameter and $8 \mathrm{ft}$ long is to be used to filter a slurry. The drum rotates at $0.5 \mathrm{rpm}$, and one-third of the drum's surface is
A plate-and-frame filter press contains 16 frames and operates at a constant flow rate of $30 \mathrm{gpm}$. Each frame has an active filtering area of $4 \mathrm{ft}^{2}$, and it takes $15

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