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applied fluid mechanics
Questions and Answers of
Applied Fluid Mechanics
A fluid sample is subjected to a "sliding plate" (simple shear) test. The area of the plates is $100 \pm 0.01 \mathrm{~cm}^{2}$ and the spacing between them is $2 \pm 0.1 \mathrm{~mm}$. When the
You want to predict how fast a glacier that is $200 \mathrm{ft}$ thick will flow down a slope inclined $25^{\circ}$ to the horizontal. Assume that the glacier ice can be described by the Bingham
Your boss gives you a sample of "gunk" and asks you to measure its viscosity. You do this in a cup and bob viscometer that has an outer (cup) diameter of 2 in., an inner (bob) diameter of $1.75
The dimensions and measured quantities in the viscometer in Problem 34 are known to the following precision:\[\begin{aligned}& \hline T: \pm 1 % \text { of full scale (full scale }=500,000 \text {
A concentrated slurry is prepared in an open $8 \mathrm{ft}$ diameter mixing tank, using an impeller with a diameter of $6 \mathrm{ft}$ located $3 \mathrm{ft}$ below the free surface. The slurry is
You would like to know the thickness of a paint film as it drains at a rate of $1 \mathrm{gpm}$ down a flat surface that is $6 \mathrm{in}$. wide and is inclined at an angle of $30^{\circ}$ to the
The following data were obtained for a proprietary salad dressing tested at $22^{\circ} \mathrm{C}$ in a cup and bob viscometer (cup diameter $=4.2 \mathrm{~cm}$, bob diameter $=4.01 \mathrm{~cm}$,
A kaolin-in-water suspension was tested in a $13 \mathrm{~mm}$ internal diameter horizontal tube, and the following data were
The same suspension as that in Problem 39 above was subsequently tested in a $28 \mathrm{~mm}$ internal diameter pipe, and the following data
The manometer equation is $\Delta \Phi=-\Delta ho g \Delta h$, where $\Delta \Phi$ is the difference in the total pressure plus static head $(P+ho g z)$ between the two points to which the manometer
A mercury manometer is used to measure the pressure drop across an orifice that is mounted in a vertical pipe. A liquid with a density of $0.87 \mathrm{~g} / \mathrm{cm}^{3}$ is flowing upward
A mercury manometer is connected between two points in a piping system that contains water. The downstream tap is $6 \mathrm{ft}$ higher than the upstream tap, and the manometer reading is $16
An inclined tube manometer with a reservoir is used to measure the pressure gradient in a large pipe carrying oil $(\mathrm{SG}=0.91)$ (see Figure $\mathrm{P} 4.5)$. The pipe is inclined at an angle
Two horizontal pipelines are parallel, with one carrying salt water $\left(ho=1.988\right.$ slugs/ $\left.\mathrm{ft}^{3}\right)$ and the other carrying fresh water $\left(ho=1.937\right.$ slugs
Two identical tanks are $3 \mathrm{ft}$ in diameter and $3 \mathrm{ft}$ high, and they are both vented to the atmosphere. The top of tank B is level with the bottom of tank A, and they are connected
An inclined tube manometer is used to measure the pressure drop in an elbow through which water is flowing (see Figure P4.10). The manometer fluid is an oil with $\mathrm{SG}=1.15$. The distance $L$
The three-fluid manometer illustrated in Figure P4.11 is used to measure a very small pressure difference $\left(P_{1}-P_{2}\right)$. The cross-sectional area of each of the reservoirs is $A$ and
A tank that is vented to the atmosphere contains a liquid with a density of $0.9 \mathrm{~g} / \mathrm{cm}^{3}$. A dip tube inserted into the top of the tank extends to a point $1 \mathrm{ft}$ from
An inclined manometer is used to measure the pressure drop between two taps on a pipe carrying water, as shown in Figure P4.13. The manometer fluid is an oil with $\mathrm{SG}=0.92$, and the
The pressure gradient required to force water through a straight horizontal $1 / 4 \mathrm{in}$. ID tube at a rate of $2 \mathrm{gpm}$ is $1.2 \mathrm{psi} / \mathrm{ft}$. Consider this same tubing
It is possible to achieve a weightless condition for a limited time in an airplane by flying in a circular arc above the earth (like a rainbow). If the plane flies at $650 \mathrm{mph}$, what should
Water is flowing in a horizontal pipe bend at a velocity of $10 \mathrm{ft} / \mathrm{s}$. The radius of curvature of the inside of the bend is 4 in., and the pipe ID is 2 in. A mercury manometer is
Calculate the atmospheric pressure at an elevation of $3000 \mathrm{~m}$, assuming (a) air is incompressible, at a temperature of $59^{\circ} \mathrm{F}$; (b) air is isothermal at $59^{\circ}
One pound mass of air $(\mathrm{MW}=29)$ at sea level and $70^{\circ} \mathrm{F}$ is contained in a balloon, which is then carried to an elevation of $10,000 \mathrm{ft}$ in the atmosphere. If the
A gas well contains hydrocarbon gases with an average molecular weight of 24 , which can be assumed to be an ideal gas with a specific heat ratio of 1.3. The pressure and temperature at the top of
The adiabatic atmosphere obeys the equation\[P / ho^{k}=\text { Constant }\]where$k$ is a constant$ho$ is densityIf the temperature decreases $0.3^{\circ} \mathrm{C}$ for every $100 \mathrm{ft}$
Using the actual dimensions of commercial steel pipe from Appendix F, plot the pipe wall thickness versus the pipe diameter for both Schedule 40 and Schedule 80 pipes, and fit the plot with a
The "yield stress" for carbon steel is 35,000 psi, and the "working stress" is one-half of this value. What schedule number would you recommend for a pipe carrying ethylene at a pressure of $2500
Consider a $90^{\circ}$ elbow in a 2 in. pipe (all of which is in the horizontal plane). A pipe tap is drilled through the wall of the elbow on the inside curve of the elbow, and another through the
A pipe carrying water is inclined at an angle of $45^{\circ}$ to the horizontal. A manometer containing a fluid with $\mathrm{SG}$ of 1.2 is attached to taps on the pipe, which are $1 \mathrm{ft}$
A tank contains a liquid of unknown density (see Figure P4.25). Two dip tubes are inserted into the tank, each to a different level in the tank, through which air is bubbled very slowly through the
The tank shown in Figure P4.26 has a partition that separates two immiscible liquids. Most of the tank contains water, and oil is floating above the water on the right of the partition. The height of
A manometer that is open to the atmosphere contains water, with a layer of oil floating on the water in one leg (see Figure P4.27). If the level of the water in the left leg is $1 \mathrm{~cm}$ above
An open cylindrical drum, with a diameter of $2 \mathrm{ft}$ and a length of $4 \mathrm{ft}$, is turned upside down in the atmosphere and then submerged in a liquid so that it floats partially
A solid spherical particle with a radius of $1 \mathrm{~mm}$ and a density of $1.3 \mathrm{~g} / \mathrm{cm}^{3}$ is immersed in water in a centrifuge. If the particle is $10 \mathrm{~cm}$ from the
A manometer with mercury as the manometer fluid is attached to the wall of a closed tank containing water (see Figure P4.30). The entire system is rotating about the axis of the tank at $N$ rpm. The
With reference to Figure P4.30, the manometer contains water as the manometer fluid and is attached to a tank that is empty and open to the atmosphere. When the tank is stationary, the water level is
You want to measure the specific gravity of a liquid. To do this, you first weigh a beaker of the liquid on a scale $\left(W_{L o}\right)$. You then attach a string to a solid body that is heavier
A vertical U-tube manometer is open to the atmosphere and contains a liquid that has a SG of 0.87 and a vapor pressure of $450 \mathrm{mmHg}$ at the operating temperature. The vertical tubes are $4
A spherical particle with $\mathrm{SG}=2.5$ and a diameter of $2 \mathrm{~mm}$ is immersed in water in a cylindrical centrifuge with a diameter of $20 \mathrm{~cm}$. If the particle is initially $8
Water is flowing into the top of a tank at a rate of $200 \mathrm{gpm}$. The tank is $18 \mathrm{in}$. in diameter and has a 3 in. diameter hole in the bottom, through which the water flows out. If
A vacuum pump operates at a constant volumetric flow rate of $10 \mathrm{~L} / \mathrm{min}$, evaluated at the pump inlet conditions. How long will it take to pump down a $100 \mathrm{~L}$ tank
Air is flowing at a constant mass flow rate into a tank that has a volume of $3 \mathrm{ft}^{3}$. The temperature of both the tank and the air is constant at $70^{\circ} \mathrm{F}$. If the pressure
A tank contains water initially at a depth of $3 \mathrm{ft}$. The water flows out of a hole in the bottom of the tank, and air at a constant pressure of $10 \mathrm{psig}$ is admitted to the top of
The flow rate of a hot coal/oil slurry in a pipeline is measured by injecting a small side stream of cool oil and measuring the resulting temperature change downstream in the pipeline. The slurry is
A gas enters a horizontal 3 in. schedule 40 pipe at a constant rate of $0.5 \mathrm{lb}_{\mathrm{m}} / \mathrm{s}$, with a temperature of $70^{\circ} \mathrm{F}$ and a pressure of $1.15
Water is flowing into the top of an open cylindrical tank (diameter $D$ ) at a volume flow rate of $Q_{i}$ and out of a hole in the bottom at a rate of $Q_{o}$. The tank is made of wood that is very
Air is flowing steadily through a horizontal tube at a constant temperature of $32^{\circ} \mathrm{C}$ and a mass flow rate of $1 \mathrm{~kg} / \mathrm{s}$. At one point upstream where the tube
Steam is flowing through a horizontal nozzle. At the inlet the velocity is $1000 \mathrm{ft} / \mathrm{s}$ and the enthalpy is $1320 \mathrm{Btu} / \mathrm{lb}_{\mathrm{m}}$. At the outlet the
Oil is being pumped from a large storage tank, where the temperature is $70^{\circ} \mathrm{F}$, through a 6 in. ID pipeline. The oil level in the tank is $30 \mathrm{ft}$ above the pipe exit. If a
Ethylene enters a 1 in. schedule 80 pipe at $170^{\circ} \mathrm{F}$ and $100 \mathrm{psia}$ and a velocity of $10 \mathrm{ft} / \mathrm{s}$. At a point somewhere downstream, the temperature has
Number 3 fuel oil $\left(30^{\circ} \mathrm{API}\right)$ is transferred from a storage tank at $60^{\circ} \mathrm{F}$ to a feed tank in a power plant at a rate of $2000 \mathrm{bbl} / \mathrm{day}$.
Oil with a viscosity of $35 \mathrm{cP}, \mathrm{SG}$ of 0.9 , and a specific heat of $0.5 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}}{ }^{\circ} \mathrm{F}\right)$ is flowing through a straight
Water is pumped at a rate of $90 \mathrm{gpm}$ by a centrifugal pump driven by a $10 \mathrm{hp}$ motor. The water enters the pump through a $3 \mathrm{in}$. sch 40 pipe at $60^{\circ} \mathrm{F}$
A pump driven by a $7.5 \mathrm{hp}$ motor takes water in at $75^{\circ} \mathrm{F}$ and $5 \mathrm{psig}$ and discharges it at $60 \mathrm{psig}$ at a flow rate of $600 \mathrm{lb}_{\mathrm{m}} /
A high-pressure pump takes water in at $70^{\circ} \mathrm{F}, 1 \mathrm{~atm}$, through a $1 \mathrm{in}$. ID suction line and discharges it at 1000 psig through a 1/8 in. ID line. The pump is
Water is contained in two closed tanks (A and B) which are connected by a pipe. The pressure in tank A is 5 psig and that in tank B is 20 psig, and the water level in tank A is $40 \mathrm{ft}$ above
A pump that is driven by a $7.5 \mathrm{hp}$ motor takes water in at $75^{\circ} \mathrm{F}$ and $5 \mathrm{psig}$ and discharges it at $60 \mathrm{psig}$ at a flow rate of $600
A $90 %$ efficient pump driven by a $50 \mathrm{hp}$ motor is used to transfer water at $70^{\circ} \mathrm{F}$ from a cooling pond to a heat exchanger through a 6 in. sch 40 pipeline. The heat
A pump takes water from the bottom of a large tank where the pressure is $50 \mathrm{psig}$ and delivers it through a hose to a nozzle that is $50 \mathrm{ft}$ above the bottom of the tank, at a rate
You have purchased a centrifugal pump to transport water at a maximum rate of $1000 \mathrm{gpm}$ from one reservoir to another through an $8 \mathrm{in}$. sch 40 pipeline. The total pressure drop
The hydraulic turbines at Boulder dam power plant are rated at $86,000 \mathrm{~kW}$ when water is supplied at a rate of $66.3 \mathrm{~m}^{3} / \mathrm{s}$. The water enters at a head of $145
Water is draining from an open conical funnel at the same rate at which it is entering the top. The diameter of the funnel is $1 \mathrm{~cm}$ at the top and is $0.5 \mathrm{~cm}$ at the bottom, and
Water is being transferred by a pump between two open tanks (from A to B) at a rate of $100 \mathrm{gpm}$. The pump receives the water from the bottom of tank A through a $3 \mathrm{in}$. sch 40 pipe
A 4 in. diameter open can has a $1 / 4$ in. diameter hole in the bottom. The can is immersed bottom down in a pool of water to a point where the bottom is $6 \mathrm{in}$. below the water surface and
Carbon tetrachloride $(\mathrm{SG}=1.6)$ is pumped at a rate of $2 \mathrm{gpm}$ through a pipe that is inclined upward at an angle of $30^{\circ}$. An inclined tube manometer (with a $10^{\circ}$
A pump that is taking water at $50^{\circ} \mathrm{F}$ from an open tank at a rate of $500 \mathrm{gpm}$ is located directly over the tank. The suction line entering the pump is a nominal 6 in. sch
A pump is transferring water from tank A to tank B, both of which are open to the atmosphere, at a rate of $200 \mathrm{gpm}$. The surface of the water in tank A is $10 \mathrm{ft}$ above ground
A surface effect (air cushion) vehicle measures $10 \mathrm{ft} \times 20 \mathrm{ft}$ and weighs $6000 \mathrm{lb}_{\mathrm{f}}$. The air is supplied by a blower mounted on top of the vehicle, which
The air cushion car in Problem 29 is equipped with a $2 \mathrm{hp}$ blower that is $70 %$ efficient.(a) What would be the clearance between the skirt of the car and the ground?(b) What is the air
An ejector pump operates by injecting a high-speed fluid stream into a slower stream to increase its pressure. Consider water flowing at a rate of $50 \mathrm{gpm}$ through a $90^{\circ}$ elbow in a
A large tank containing water has a $51 \mathrm{~mm}$ diameter hole in the bottom. When the depth of the water is $15 \mathrm{~m}$ above the hole, the flow rate through the hole is found to be
Water at $68^{\circ} \mathrm{F}$ is pumped through a $1000 \mathrm{ft}$ length of 6 in. sch 40 pipe. The discharge end of the pipe is $100 \mathrm{ft}$ above the suction end. The pump is $90 %$
You want to siphon water out of a large tank using a 5/8 in. ID hose. The highest point of the hose is $10 \mathrm{ft}$ above the water surface in the tank, and the hose exit outside the tank is $5
It is desired to siphon a volatile liquid out of a deep open tank. If the liquid has a vapor pressure of $200 \mathrm{mmHg}$ and a density of $45 \mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}$ and the
The propeller of a speedboat is $1 \mathrm{ft}$ in diameter and $1 \mathrm{ft}$ below the surface of the water. At what speed (rpm) will cavitation occur? The vapor pressure of the water is $18.65
A conical funnel is full of liquid. The diameter of the top (mouth) is $D_{1}$, and that of the bottom (spout) is $D_{2}$ (where $D_{2} \ll D_{1}$ ), and the depth of the fluid above the bottom is
An open cylindrical tank of diameter $D$ contains a liquid of density $ho$ at a depth $H$. The liquid drains through a hole of diameter $d$ in the bottom of the tank. The velocity of the liquid
An open cylindrical tank, that is $2 \mathrm{ft}$ in diameter and $4 \mathrm{ft}$ high is full of water. If the tank has a 2 in. diameter hole in the bottom, how long will it take for half of the
A large tank has a $5.1 \mathrm{~mm}$ diameter hole in the bottom. When the depth of liquid in the tank is $1.5 \mathrm{~m}$ above the hole, the flow rate through the hole is found to be $324
A window is left slightly open while the air conditioning system is running. The air conditioning blower develops a pressure of 2 in. $\mathrm{H}_{2} \mathrm{O}$ (gage) inside the house, and the
Water at $68^{\circ} \mathrm{F}$ is pumped through a $1000 \mathrm{ft}$ length of $6 \mathrm{in}$. sch 40 pipe. The discharge end of the pipe is $100 \mathrm{ft}$ above the suction end. The pump is
The plumbing in your house is $3 / 4$ in. sch 40 galvanized pipe, and it is connected to an 8 in. sch 80 water main in which the pressure is $15 \mathrm{psig}$. When you turn on a facet in your
A $60 %$ efficient pump driven by a $10 \mathrm{hp}$ motor is used to transfer bunker $\mathrm{C}$ fuel oil from a storage tank to a boiler through a well-insulated line. The pressure in the tank is
You have probably noticed that when you turn on the garden hose, it will whip about uncontrollably if it is not restrained. This is because of the unbalanced forces developed by the change of
Repeat Problem 45 for the case in which a nozzle is attached to the end of the hose and the water exits the nozzle through a 1/4 in. opening. The loss coefficient for the nozzle is 0.3 based on the
You are watering your garden with a hose that has a $3 / 4 \mathrm{in}$. ID, and the water is flowing at a rate of $10 \mathrm{gpm}$. A nozzle attached to the end of the hose has an ID of $1 / 4
A 4 in. ID fire hose discharges water at a rate of $1500 \mathrm{gpm}$ through a nozzle that has a $2 \mathrm{in}$. ID exit. The nozzle is conical and converges through a total included angle of
A $90^{\circ}$ horizontal reducing bend has an inlet diameter of $4 \mathrm{in}$. and an outlet diameter of $2 \mathrm{in}$. If water enters the bend at a pressure of $40 \mathrm{psig}$ and a flow
A fireman is holding the nozzle of a fire hose that he is using to put out a fire. The hose is 3 in. in diameter, and the nozzle is $1 \mathrm{in}$. in diameter. The water flow rate is $200
Water flows through a $30^{\circ}$ pipe bend at a rate of $200 \mathrm{gpm}$. The diameter of the entrance to the bend is $2.5 \mathrm{in}$. and that of the exit is $3 \mathrm{in}$. The pressure in
A nozzle with a $1 \mathrm{in}$. ID outlet is attached to a $3 \mathrm{in}$. ID fire hose. Water pressure inside the hose is $100 \mathrm{psig}$ and the flow rate is $100 \mathrm{gpm}$. Calculate the
Water flows through a $45^{\circ}$ expansion pipe bend at a rate of $200 \mathrm{gpm}$, exiting into the atmosphere. The inlet to the bend is $2 \mathrm{in}$. ID, the exit is $3 \mathrm{in}$. ID, and
A patrol boat is powered by a water jet engine, which takes water in at the bow through a $1 \mathrm{ft}$ diameter duct and pumps it out the stern through a 3 in. diameter exhaust jet. If the water
A patrol boat is powered by a water jet pump engine. The engine takes water in through a $3 \mathrm{ft}$ diameter duct in the bow and discharges it through a $1 \mathrm{ft}$ diameter duct in the
Water is flowing through a $45^{\circ}$ pipe bend at a rate of $200 \mathrm{gpm}$ and exits into the atmosphere. The inlet to the bend is $1 \frac{1}{2} \mathrm{in}$. inside diameter, and the exit is
The arms of a lawn sprinkler are 8 in. long and $3 / 8$ in. ID. Nozzles at the end of each arm direct the water in a direction that is $45^{\circ}$ from the arms. If the total flow rate is $10
A water sprinkler contains two $1 / 4 \mathrm{in}$. ID jets at the ends of a rotating hollow ( $3 / 8 \mathrm{in}$. ID) tube, which direct the water $90^{\circ}$ to the axis of the tube. If the water
An open container $8 \mathrm{in}$. high with an inside diameter of $4 \mathrm{in}$. weighs $5 \mathrm{lb}_{\mathrm{f}}$ when empty. The container is placed on a scale and water flows into the top of
A boat is tied to a dock by a line from the stern of the boat to the dock. A pump inside the boat takes water in through the bow and discharges it out the stern at a rate of $3 \mathrm{ft}^{3} /
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