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applied fluid mechanics
Questions and Answers of
Applied Fluid Mechanics
A jet ejector pump is shown in Figure P5.61. A high-speed stream $\left(Q_{A}\right)$ is injected at a rate of $50 \mathrm{gpm}$ through a small tube $1 \mathrm{in}$. in diameter, into a stream
Figure P5.62 illustrates two relief valves. The valve disk is designed to lift when the upstream pressure in the vessel $\left(P_{1}\right)$ reaches the valve set pressure. Valve $\mathrm{A}$ has a
A relief valve is mounted on top of a large vessel containing hot water. The inlet diameter to the valve is 4 in., and the outlet diameter is 6 in. The valve is set to open when the pressure in the
A relief valve is installed on the bottom of a pressure vessel. The entrance to the valve is $4.5 \mathrm{in}$. diameter and the exit (which discharges in the horizontal direction, $90^{\circ}$ from
An emergency relief valve is installed on a reactor to relieve excess pressure in case of a runaway reaction. The lines upstream and downstream of the valve are 6 in. sch 40 pipe. The valve is
Consider the "tank on wheels" shown in Figure P5.66. Water is draining out of a hole in the side of the open tank, at a rate of $10 \mathrm{gpm}$. If the tank diameter is $2 \mathrm{ft}$ and the
The tank in Problem 66 is 6 in. in diameter and contains water at a depth of $3 \mathrm{ft}$. On the side of the tank near the bottom is a $1.5 \mathrm{in}$. ID outlet to which is attached a ball
Use the microscopic equations of motion in Appendix $\mathrm{E}$ as a starting point to derive a relationship between the volumetric flow rate and the pressure gradient for a Newtonian fluid in a
A viscous molten polymer is pumped through a thin slit between two flat surfaces. The slit has a depth $H$, width $W$, and length $L$, and is inclined upward at an angle $\theta$ to the horizontal
Acrylic latex paint can be described as a Bingham plastic with a yield stress of $200 \mathrm{dyn} / \mathrm{cm}^{2}$, a limiting viscosity of $50 \mathrm{cP}$, and a density of $0.95 \mathrm{~g} /
A vertical belt is moving upward continuously through a liquid bath at a velocity $V$. A film of the liquid adheres to the belt, which tends to drain downward due to gravity. The equilibrium
Water at $70^{\circ} \mathrm{F}$ flows upward through a vertical tube and overflows over the top and down the outside wall. The OD of the tube is 4 in., and the water flow rate is $1 \mathrm{gpm}$.
For laminar flow of a Newtonian fluid in a tube(a) Show that the average velocity over the cross section is half of the maximum velocity in the tube.(b) Derive the kinetic energy correction factor
A slider bearing can be described as one plate moving with a velocity $V$ parallel to a stationary plate, with a viscous lubricant in between the plates. The force applied to the moving plate is $F$,
Consider a fluid flowing in a conical section, as illustrated in Figure P5.75. The mass flow rate is the same going in (through point 1) as it is coming out (point 2), but the velocity changes
Show how the Hagen-Poiseuille equation for the steady laminar flow of a Newtonian fluid in a uniform cylindrical tube can be derived starting from the general microscopic equations of motion (e.g.,
The Hagen-Poiseuille equation (Equation 6.11) describes the laminar flow of a Newtonian fluid in a tube. Since a Newtonian fluid is defined by the relation $\tau=\mu \dot{\gamma}$, rearrange the
Derive the relation between the friction factor and Reynolds number in turbulent flow for smooth pipe (Equation 6.34), starting with the von Karman equation for the velocity distribution in the
Evaluate the kinetic energy correction factor $\alpha$ in the Bernoulli equation for turbulent flow assuming the $1 / 7$ power law velocity profile (Equation 6.36) is valid. Repeat this for laminar
A Newtonian fluid with $\mathrm{SG}=0.8$ is forced through a capillary tube at a rate of $5 \mathrm{~cm}^{3} / \mathrm{min}$. The tube has a downward slope of $30^{\circ}$ to the horizontal, and the
A liquid is draining from a cylindrical vessel through a tube in the bottom of the vessel, as illustrated in Figure P6.6 below. If the liquid has a specific gravity of 0.85 and drains out at a rate
Repeat problem 7 accounting for the friction loss from the vessel to the tube, assuming a loss coefficient of 0.50 at the contraction.problem 7,You are given a liquid and are asked to find its
You must measure the viscosity of an oil that has an SG of 0.92 . To do this, you put the oil into a large container to the bottom of which a small vertical tube, $25 \mathrm{~cm}$ long, has been
You want to transfer No. 3 fuel oil $\left(30^{\circ} \mathrm{API}\right)$ from a storage tank to a power plant at a rate of $2000 \mathrm{bbl} / \mathrm{day}$. The diameter of the pipeline is $1
You must specify a pump to deliver $800 \mathrm{bbl} /$ day of a $35^{\circ} \mathrm{API}$ distillate at $90^{\circ} \mathrm{F}$ from a distillation column to a storage tank in a refinery. If the
Water is flowing at a rate of $700 \mathrm{gpm}$ through a horizontal 6 in. sch 80 commercial steel pipe at $90^{\circ} \mathrm{F}$. If the pressure drops by 2.23 psi over a $100 \mathrm{ft}$ length
A $35^{\circ}$ API distillate at $60^{\circ} \mathrm{F}$ is to be pumped over a distance of $2000 \mathrm{ft}$ through a $4 \mathrm{in}$. sch 40 horizontal pipeline at a flow rate of $500
The Moody diagram illustrates the effect of roughness on the friction factor in turbulent flow but indicates no effect of roughness in laminar flow. Explain why this is so. Are there any restrictions
You have a large supply of very rusty $2 \mathrm{in}$. sch 40 steel pipe, which you want to use for a pipeline. Because rusty metal is rougher than clean metal, you want to know its effective
A $32 \mathrm{hp}$ pump ( $100 %$ efficient) is required to pump water through a 2 in. sch 40 pipeline, $6000 \mathrm{ft}$ long, at a rate of $100 \mathrm{gpm}$.(a) What is the equivalent roughness
You have a piping system in your plant that has gotten old and rusty. The pipe is $2 \mathrm{in}$. sch 40 steel, $6000 \mathrm{ft}$ long. You find that it takes $35 \mathrm{hp}$ to pump water through
Water enters a horizontal tube through a flexible vertical rubber hose that can support no forces. If the tube is $1 / 8 \mathrm{in}$. sch $40,10 \mathrm{ft}$ long, and the water flow rate is $2
A water tower that is $90 \mathrm{ft}$ high provides water to a residential subdivision. The water main from the tower to the subdivision is $6 \mathrm{in}$. sch 40 steel, 3 miles long. If each house
A heavy oil $(\mu=100 \mathrm{cP}, \mathrm{SG}=0.85)$ is draining from a large tank through a $1 / 8 \mathrm{in}$. sch 40 tube into an open bucket. The level in the tank is $3 \mathrm{ft}$ above the
SAE 10 lube oil $(\mathrm{SG}=0.93)$ is being pumped upward through a straight $1 / 4 \mathrm{in}$. sch 80 pipe that is oriented at $45^{\circ}$ angle to the horizontal. The two legs of a manometer
Cooling water is fed by gravity from an open storage tank $20 \mathrm{ft}$ above ground, through $100 \mathrm{ft}$ of $1 \frac{1}{2}$ in. ID steel pipe, to a heat exchanger at ground level. If the
A water main is to be laid to supply water to a subdivision located 2 miles from a water tower. The water in the tower is $150 \mathrm{ft}$ above ground, and the subdivision consumes a maximum of
A water main is to be laid from a water tower to a subdivision that is 2 miles away. The water level in the tower is $150 \mathrm{ft}$ above the ground. The main must supply a maximum of $1000
The water level in a water tower is $110 \mathrm{ft}$ above ground level. The tower supplies water to a subdivision, 3 miles away, through an 8 in. sch 40 steel water main. If the minimum water
A hydraulic press is powered by a remote high-pressure pump. The gage pressure at the pump is $20 \mathrm{MPa}$, and the pressure required to operate the press is $19 \mathrm{MPa}$ (gage) at a flow
Water is to be pumped at a rate of $100 \mathrm{gpm}$ from a well that is $100 \mathrm{ft}$ deep, through 2 miles of horizontal 4 in. sch 40 steel pipe, to a water tower that is $150 \mathrm{ft}
A concrete pipe storm sewer, $4 \mathrm{ft}$ in diameter, drops $3 \mathrm{ft}$ in elevation per mile of length. What is the maximum capacity of the sewer (in gpm) when it is flowing full?
You want to siphon water from an open tank using a 1/4 in. diameter hose. The discharge end of the hose is $10 \mathrm{ft}$ below the water level in the tank, and the siphon will not operate if the
Equation 6.43 describes the laminar flow of a power law fluid in a tube. Since a power law fluid is defined by the relation $\tau=m \dot{\gamma}^{n}$, rearrange Equation 6.43 to show that the shear
A large tank contains SAE 10 lube oil at a temperature of $60^{\circ} \mathrm{F}$ and a pressure of $2 \mathrm{psig}$. The oil is $2 \mathrm{ft}$ deep in the tank and drains out through a vertical
A polymer solution is to be pumped at a rate of $3 \mathrm{gpm}$ through a horizontal $1 \mathrm{in}$. diameter pipe. The solution behaves as a power law fluid with a flow index of 0.5 , an apparent
A coal slurry that is characterized as a power law fluid has a flow index of 0.4 and an apparent viscosity of $200 \mathrm{cP}$ at a shear rate of $1 \mathrm{~s}^{-1}$. If the coal has a specific
A coal slurry is found to behave as a power law fluid, with a flow index of 0.3 , a specific gravity of 1.5 , and an apparent viscosity of $70 \mathrm{cP}$ at a shear rate of $100 \mathrm{~s}^{-1}$.
A coal slurry is to be transported by pipeline. It has been determined that the slurry may be described by the power law model, with a flow index of 0.4 , an apparent viscosity of $50 \mathrm{cP}$ at
A sewage sludge is to be transported a distance of $3 \mathrm{mi}$ through a $12 \mathrm{in}$. ID pipeline at a rate of $2000 \mathrm{gpm}$. The sludge is a Bingham plastic with a yield stress of $35
A coal suspension is found to behave as a power law fluid, with a flow index of 0.4 , a specific gravity of 1.5 , and an apparent viscosity of $90 \mathrm{cP}$ at a shear rate of $100
A coal-water slurry containing $65 %$ (by weight) coal is pumped from a storage tank at a rate of $15 \mathrm{gpm}$ through a $50 \mathrm{~m}$ long $1 / 2 \mathrm{in}$. sch 40 pipeline to a boiler
A sludge is to be transported by pipeline. It has been determined that the sludge may be described by the power law model, with a flow index of 0.6 , an apparent viscosity of $50 \mathrm{cP}$ at a
You must design a transfer system to feed a coal slurry to a boiler. However, you don't know the slurry properties, so you measure them in the lab using a cup and bob (Couette) viscometer. The cup
A thick slurry with $S G=1.3$ is to be pumped through a $1 \mathrm{in}$. ID pipe that is $200 \mathrm{ft}$ long. You don't know the properties of the slurry, so you test it in the lab by pumping it
Drilling mud has to be pumped down into an oil well that is $8000 \mathrm{ft}$ deep. The mud is to be pumped at a rate of $50 \mathrm{gpm}$ to the bottom of the well and back to the surface, through
A straight vertical tube, $100 \mathrm{~cm}$ long and $2 \mathrm{~mm}$ ID, is attached to the bottom of a large vessel. The vessel is open to the atmosphere and contains a liquid with a density of $1
A non-Newtonian fluid, described by the power law model, is flowing through a thin slit between two parallel planes of width $W$, separated by a distance $H$. The slit is inclined upward at an angle
You are drinking a milk shake through a straw that is $8 \mathrm{in.}$ long and $0.3 \mathrm{in}$. in diameter. The milk shake has the properties of a Bingham plastic, with a yield stress of $300
Water is to be transferred at a rate of $500 \mathrm{gpm}$ from a cooling lake through a $6 \mathrm{in}$. diameter sch 40 pipeline to an open tank in a plant that is 30 miles from the lake.(a) If the
You measure the viscosity of a sludge in the lab and conclude that it can be described as a power law fluid with a flow index of 0.45 , a viscosity of 7 poise at a shear rate of $1 \mathrm{~s}^{-1}$,
An open drum, $3 \mathrm{ft}$ in diameter, contains a mud that is known to be described by the Bingham plastic model, with a yield stress of $120 \mathrm{dyn} / \mathrm{cm}^{2}$, a limiting viscosity
You would like to determine the pressure drop-flow rate relation for a slurry in a pipeline. To do this, you must determine the rheological properties of the slurry, so you test it in the lab by
A pipeline is installed to transport a red mud slurry from an open tank in an alumina plant to a disposal pond. The line is $5 \mathrm{in}$. sch 80 commercial steel, 12,000 ft long, and is designed
Determine the power required to pump water at a rate of $300 \mathrm{gpm}$ through a $3 \mathrm{in}$. ID pipeline, $50 \mathrm{mi}$ long, if(a) The pipe is new commercial steel(b) The pipe wall is
You must size a pipeline to carry crude oil at a rate of 1 million bbl/day. If the viscosity of the oil is $25 \mathrm{cP}$ and its $\mathrm{SG}$ is 0.9 , what is the most economical diameter for the
A crude oil pipeline is to be built to carry oil at a rate of 1 million $\mathrm{bbl} / \mathrm{day}(1 \mathrm{bbl}=42 \mathrm{gal})$. If the pipe cost $\$ 12 / \mathrm{ft}$ of length per inch of
A coal slurry pipeline is to be built to transport 45 million tons/year of slurry over a distance of 1500 miles. The slurry can be approximately described as Newtonian with a viscosity of $35
The Alaskan pipeline was designed to carry crude oil at a rate of 1.2 million $\mathrm{bbl} / \mathrm{day}(1 \mathrm{bbl}=$ $42 \mathrm{gal})$. If the oil is assumed to be Newtonian, with a viscosity
What is the most economical diameter of a pipeline that is required to transport crude oil $(\mu=$ $30 \mathrm{cP}, \mathrm{SG}=0.95)$ at a rate of 1 million bbl/day using ANSI 1500\# pipe if the
Find the most economical diameter of Sch. 40 commercial steel pipe that would be needed to transport a petroleum fraction with a viscosity of $60 \mathrm{cP}$ and $\mathrm{SG}$ of 1.3 at a rate of
You must design and specify equipment for transporting $100 %$ acetic acid (density $=1000 \mathrm{~kg} / \mathrm{m}^{3}$, $\mu=1 \mathrm{mPa}$ s), at a rate of $11.3 \mathrm{~m}^{3} / \mathrm{h}$,
A large building has a roof with dimensions $50 \mathrm{ft} \times 200 \mathrm{ft}$, which drains into a gutter system. The gutter contains three drawn aluminum downspouts that have a square cross
A roof drains into a gutter, which feeds into a downspout with a square cross section (4 in. $x$ 4 in.). The discharge end of the downspout is $12 \mathrm{ft}$ below the entrance and terminates in a
An open concrete flume is to be constructed to carry water from a plant unit to a cooling lake by gravity flow. The flume has a square cross section and is $1500 \mathrm{ft}$ long. The elevation at
An open drainage canal with a rectangular cross section is $3 \mathrm{~m}$ wide and $1.5 \mathrm{~m}$ deep. If the canal slopes $950 \mathrm{~mm}$ in $1 \mathrm{~km}$ of length, what is the maximum
A concrete-lined drainage ditch has a triangular cross section that is an equilateral triangle, $8 \mathrm{ft}$ on each side. The ditch has a slope of $3 \mathrm{ft} / \mathrm{mile}$. What is the
An open drainage canal is to be constructed to carry water at a maximum rate of $10^{6} \mathrm{gpm}$. The canal is concrete lined and has a rectangular cross section, with a width that is twice its
A drainage ditch is to be built to carry runoff from a subdivision. The maximum design capacity is to be $1 \mathrm{million} \mathrm{gph}(\mathrm{gal} / \mathrm{h})$ and it is to be concrete lined.
A drainage canal is to be dug to keep a low-lying area from flooding during heavy rains. The canal would carry the water to a river that is 1 mile away and $6 \mathrm{ft}$ lower in elevation. The
An open drainage canal with a rectangular cross section and a width of $20 \mathrm{ft}$ is lined with concrete. The canal has a slope of $1 \mathrm{ft} / 1000$ yards. What is the depth of water in
An air ventilating system must be designed to deliver air at $20^{\circ} \mathrm{F}$ and atmospheric pressure at a rate of $150 \mathrm{ft}^{3} / \mathrm{s}$ through $4000 \mathrm{ft}$ of square
Oil with a viscosity of $25 \mathrm{cP}$ and $\mathrm{SG}$ of 0.78 is stored in a large open tank. A vertical tube made of stainless steel with an ID of $1 \mathrm{in}$. and a length of $6
A vertical tube is attached to the bottom of an open vessel. A liquid with an $\mathrm{SG}$ of 1.2 is draining through the tube, which is $10 \mathrm{~cm}$ long with an ID of $3 \mathrm{~mm}$. When
Heat is to be transferred from one process stream to another by means of a double pipe heat exchanger. The hot fluid flows in a $1 \mathrm{in}$. Sch. 40 tube, which is inside (and concentric with) a
A commercial steel pipe ( $\varepsilon=0.0018 \mathrm{in}$.) is $1 \frac{1}{2} \mathrm{in}$. Sch. 40 diameter, $50 \mathrm{ft}$ long, and includes one globe valve. If the pressure drop across the
Water at $68^{\circ} \mathrm{F}$ is flowing through a $45^{\circ}$ pipe bend at a rate of $2000 \mathrm{gpm}$. The inlet to the bend is $3 \mathrm{in}$. ID, and the outlet is $4 \mathrm{in}$. ID. The
What size pump (horsepower) is required to pump an organic product ( $\mathrm{SG}=0.85$ and $\mu=60 \mathrm{cP}$ ) from tank A to tank B at a rate of $2000 \mathrm{gpm}$ through a $10 \mathrm{in}$.
A plant piping system takes a process stream $\left(\mu=15 \mathrm{cP}, ho=0.9 \mathrm{~g} / \mathrm{cm}^{3}\right)$ from one vessel at $20 \mathrm{psig}$ and delivers it to another vessel at $80
The Alaskan pipeline is 48 in. ID, 800 miles long, and carries crude oil at a rate of $1.2 \mathrm{million} \mathrm{bbl} / \mathrm{day}(1 \mathrm{bbl}=42 \mathrm{gal}$ ). Assuming the crude oil to be
A 6 in. Sch. 40 pipeline carries an intermediate product stream $(\mu=15 \mathrm{cP}, \mathrm{SG}=0.85)$ at a velocity of $7.5 \mathrm{ft} / \mathrm{s}$ from a storage tank at $1 \mathrm{~atm}$
An open tank contains $5 \mathrm{ft}$ of water. The tank drains through a piping system containing $1090^{\circ}$ elbows, 10 branched tees, 6 gate valves, and $40 \mathrm{ft}$ of horizontal Sch. 40
A pump takes water from a reservoir and delivers it to a water tower. The water in the tower is at atmospheric pressure and is $120 \mathrm{ft}$ above the reservoir. The pipeline is composed of $1000
You must determine the pump head and power required to transport a petroleum fraction $(\mu=$ $\left.60 \mathrm{cP}, ho=55 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}\right)$ at a rate of $500
What horsepower pump would be required to transfer water at a flow rate of $100 \mathrm{gpm}$ from tank A to tank B, if the liquid surface in tank A is $8 \mathrm{ft}$ above ground and that in tank B
An additive having a viscosity of $2 \mathrm{cP}$ and a density of $50 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$ is fed from a reservoir into a mixing tank. The pressure in both the reservoir and
The pressure in the water main serving your house is $90 \mathrm{psig}$. The plumbing between the main and your outside faucet contains $250 \mathrm{ft}$ of galvanized $3 / 4$ in. Sch. 40 pipe, 16
You are filling your beer mug from a keg. The pressure in the keg is $5 \mathrm{psig}$, the filling tube from the keg is $3 \mathrm{ft}$ long and $1 / 4 \mathrm{in}$. ID, and the valve is a diaphragm
You must install a piping system to drain $\mathrm{SAE} 10$ lube oil at $70^{\circ} \mathrm{F}(\mathrm{SG}=0.928)$ from tank $\mathrm{A}$ to tank B by gravity flow. The level in tank A is $10
A new industrial plant requires a supply of water at a rate of $5.7 \mathrm{~m}^{3} / \mathrm{min}$. The pressure in the water main is $800 \mathrm{kPa}$, and it is $50 \mathrm{~m}$ from the plant.
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