Questions and Answers of Fundamentals Of Chemical Engineering Thermodynamics

The hydrodynamic boundary layer equations consist of one momentum equation and the continuity equation. How does one solve for the pressure?
How does the hydrodynamic boundary layer thickness depend upon the Reynolds number?
In laminar flow, why does the heat transfer coefficient decrease as the boundary layer thickness grows?
If the liquid has a high thermal conductivity, the heat transfer coefficient depends on \(\mathrm{Pr}^{1 / 2}\). What is the root cause of the increase dependence on \(\mathrm{Pr}\) ?
Compared with forced convection, in natural convection, the boundary layer thickness grows much more slowly. Why does this occur and what replaces the Reynolds number as a measure of the flow?
At high mass transfer rates, the mass transfer coefficient depends on both the magnitude and direction of mass transfer. Why?
Consider a flat plate moving across the surface of water with a velocity of \(5 \mathrm{~m} / \mathrm{s}\). The dimensions of the plate are \(2 \mathrm{~m} \times 2 \mathrm{~m}\).a. Calculate the
The boundary layer analysis performed in Section 12.6.1 assumed that the fluid was flowing over a stationary plate. However, there is no reason why the fluid cannot be quiescent while the plate moves
We introduced the concept of lift in conjunction with potential flow about a sphere. Plate-like objects such as your hand outside a moving car window also experience lifting force depending upon your
Based on pure aerodynamics of the type mentioned in problem 12.9, bumblebees are not supposed to be able to fly. Assume that the average bumblebee has a mass of about \(0.9 \mathrm{~g}\), a wingspan
You are evaluating a laboratory report from a senior chemical engineering student. The lab involves measuring the local friction factor over a flat plate. The student states that a plot of \(C_{f
The momentum boundary layer equations were solved to obtain expressions for the velocity profile. Use this information to calculate:a. The velocity potential.b. The stream function.c. The vorticity.
To control the drag force or the rate of heat transfer to a surface, a technique called transpirational cooling is employed. The situation is shown in Figure P12.13. The surface of the substrate to
A sailboard is gliding across a lake at a speed of \(1 \mathrm{mph}(0.45 \mathrm{~m} / \mathrm{s})\). The sailboard is \(0.3 \mathrm{~m}\) long, \(1 \mathrm{~m}\) wide and represents a smooth, flat
Consider the case of flow over a flat plate where we have a constant pressure drop across the plate \((\partial P / \partial x=\Delta P / L ; \partial P / \partial y=0)\). Rework the integral
Using a linear velocity profile for the velocity within the boundary layer, use our boundary integral analysis to derive a new expression for the friction number, \(N_{f}\). How does \(N_{f}\) depend
We want to see the effect of wind speed on the heat transfer coefficient between a human body and air. Calculate the average heat transfer coefficient at three different air velocities: \(1
A flat plate \(100 \mathrm{~cm}\) long and \(150 \mathrm{~cm}\) wide is held at a temperature of \(20^{\circ} \mathrm{C}\). The plate is immersed in an air stream at \(40^{\circ} \mathrm{C}\) and \(1
A finned tube is to be used for a heat transfer operation that involves engine oil. The tube and fins are made of copper with the fins being \(4 \mathrm{~cm}\) on a side and \(1 \mathrm{~mm}\) thick.
A new fractal surface is being developed for heat transfer by Crinkle, Inc. It is projected to revolutionize the home heating industry. As an agent of Industrial Espionage Ltd., you have stolen some
It's a sunny winter day. In your haste to get to an exam you accidentally lock Rover in the car. The interior dimensions are \(\left(L=2 \mathrm{~m}\right.\), Area \(=2.5 \mathrm{~m}^{2}\), Volume
The temperature profile in the boundary layer for air flowing over a heated surface has been found to obey:\[\frac{T-T_{s}}{T_{\infty}-T_{s}}=1-\exp \left[-\operatorname{Pr}\left(\frac{v_{\infty}
A thin, \(0.1 \mathrm{~m}\) thick plate of copper is brought into contact with a flowing water stream as shown in Figure P12.23. What is the temperature at the center of the plate, 10 minutes later?
Atmospheric air is in parallel flow \(\left(v_{\infty}=15 \mathrm{~m} / \mathrm{s}, T_{\infty}=15^{\circ} \mathrm{C}\right)\) over a flat heater surface that is to be maintained at \(140^{\circ}
For flow over a flat plate with an extremely rough surface, convection heat transfer effects are known to be correlated by the expression\[N u_{x}=0.04 \operatorname{Re}_{x}^{0.9}
Consider flow over a flat plate where the surface of the plate has a temperature distribution. Here we are solving the situation for the unheated starting length but once the plate is heated, the
Building on the previous problem allows us to look at predicting the temperature distribution for an arbitrary heat-flux specification at the surface. Here we can solve for the temperature
You are taking a shower in your normally unheated bathroom. It's winter and you notice an extreme amount of condensation on the walls. Given the following information, calculate:a. The velocity
Flow along a flat plate is occurring in a situation where both forced convection and natural convection happen. Assuming natural convection is important when the heat transfer coefficient is \(>10
The temperature profile in the boundary layer \(0.1 \mathrm{~m}\) from the leading edge of the plate was measured by a hot-wire anemometer and is shown in Figure P12.30. If the fluid is water, the
On a flat plate, the concentration profile was measured and can be represented by the following function:\[\frac{C_{a}-C_{a s}}{C_{a \infty}-C_{a s}}=1+\left(1.2-\frac{y}{v}\right)^{\frac{1}{2}}\]If
Equation (12.265) indicates that the magnitude and direction of mass transfer can have a large effect on the Sherwood number. It is interesting to explore this a bit. Consider two situations. In the
Wettability gradients are present in many biological systems and have been used to do interesting things like make water run uphill [29]. One way to form such a surface on glass is to immerse the
A fluid flows along a flat, horizontal plate which is slightly soluble in the liquid. At a distance, \(x=10 \mathrm{~cm}\) from the leading edge of the plate, the concentration boundary layer
A puddle of water \(1 \mathrm{~m}\) in diameter and \(1 \mathrm{~cm}\) deep sits on your driveway. The air temperature is \(20^{\circ} \mathrm{C}\) and a slight breeze is blowing at \(4 \mathrm{~m} /
Consider the situation where we have a flat plate dissolving into the boundary layer. To assist the dissolution process, we treat the fluid so that it contains a reactive component that complexes
A fluid containing a solute, \(a\), in dilute solution flows over a flat plate. The solute adsorbs on the plate at a rate characterized by:\[-r_{a}=\frac{k^{\prime \prime} c_{a}}{1+K c_{a}}\]Repeat
A large plate, \(0.25 \mathrm{~m}\) in diameter, is coated with a \(1 \mathrm{~mm}\) layer of zeolite catalytic material. A gas containing a noxious compound is slowly flowing over the catalytic
Consider fully developed transport in a circular tube. Explain why the Nusselt number, Sherwood number, and friction factor are constants (in the axial direction). Would you expect the same behavior
Consider the composite tube shown in Figure P13.2. Which segment of the tube should have the highest heat transfer coefficient, \(h\) ? The highest friction factor, \(C f\) ? Why? FIGURE P13.2 d d2>
Heat transfer coefficients about a sphere or cylinder are highest at the forward stagnation point and decrease as one moves about the object toward the boundary layer separation point. Why?
In our discussion of dispersion, we mentioned it can also be applied for the heat transfer case. Comparing mass vs. thermal diffusivities, for what fluids might thermal dispersion be important? Is
Does a drag coefficient exist for flows induced by natural convection? If so, what primary dimensionless quantity might such a drag coefficient depend upon?
A student wishes to perform an experiment on terminal velocities. He suspends a spherical-tipped caplet above a vat of water and then drops it end-on and then transversely into the water noting the
Formula One cars are the fastest open-wheel racing cars in the world. An F138 Ferrari Formula One car has a top speed of \(360 \mathrm{~km} / \mathrm{hr}\). The frontal area of the car is \(1.0
Two bodies are immersed in a flowing air stream at \(300 \mathrm{~K}\) and \(1 \mathrm{~atm}\). The first is a sphere of diameter \(1 \mathrm{~m}\) and the second is a cylinder of diameter \(0.5
In this era of "sustainability," driving a car has become a serious issue. One proposed solution is the introduction of hybrid cars. For example, the fuel economy for Toyota Camry and Honda Civic
A viscous fluid flows slowly by gravity down a \(2 \mathrm{~cm}\) diameter galvanized iron pipe. The pressures at the higher and lower locations are \(120 \mathrm{kPa}\) and \(130 \mathrm{kPa}\),
Tumbleweeds move by rolling across the ground, driven by the drag force they experience when exposed to a breeze. Such a concept has been proposed for developing planetary exploration vehicles to be
The bacterium, Thiovulum majus, a species that metabolizes sulfur, is about \(18 \mu \mathrm{m}\) in diameter and can swim, if provoked, at speeds of up to \(600 \mu \mathrm{m} / \mathrm{s}\). We
A simple way of measuring the drag force is shown in Figure P13.13. An object, in this case a sphere of weight, \(W\), and diameter, \(d\), is suspended using a relatively weightless wire of length,
Hail is formed when ice particles from the upper layers of a thunderstorm fall through the rain, pick up a layer of water, and then get caught in the updraft of the storm which freezes the
The drag coefficient for irregularly shaped objects was measured as a function of Reynolds number. The objects were made into equivalent spheres for calculating the Reynolds number. The table below
Air at \(40^{\circ} \mathrm{C}\) flows over a long, \(25 \mathrm{~mm}\) diameter cylinder with an embedded electrical heater. Measurements of the effect of the free stream velocity, \(v_{\infty}\),
A very large fermenter is supplied with oxygen sparged in at the bottom to run an aerobic fermentation. Proper control of the device requires that we be able to estimate the percent oxygen
A crystal is growing from a supersaturated solution at a rate of \(0.2 \mu \mathrm{m} / \mathrm{s}\). The solution contains 4 moles/lit of solute and saturated conditions have been measured to be
The temperature of a liquid stream in a heat exchanger is determined by thermocouples as shown in Figure P13.20. One thermocouple is attached to the tube wall and it measures a temperature of \(300
A new spray-painting system is being evaluated for the auto industry. The paint is delivered via an atomizer that produces \(10 \mu \mathrm{m}\) particles and propels them toward the surface at a
Spherical polymer pellets impregnated with hormones or other proteins are being investigated as implants to deliver therapeutic agents directly to an affected area. In general, when the agent is
A \(50 \mathrm{~mm}\) diameter, thin-walled tin tube is shown in the figure below. The tube is covered with a \(20 \mathrm{~mm}\) thick layer of insulation \(\left(k_{i}=0.05 \mathrm{~W} / \mathrm{m}
An insulated tube carries hot water. The tube is \(2 \mathrm{~cm}\) in diameter (inside), \(100 \mathrm{~m}\) long, and the flow rate of fluid is \(0.5 \mathrm{~kg} / \mathrm{min}\). The tube is made
Water, initially at \(25^{\circ} \mathrm{C}\), is slowly flowing through a \(1 \mathrm{~cm}\) diameter tube whose wall temperature remains constant at \(-10^{\circ} \mathrm{C}\). The water velocity
The entry length problem discussed in Section 13.5.1 can be analyzed using the boundary layer equations for a flat plate. The only caveat is that the thermal boundary layer must be small compared to
Consider fully developed flow inside the annulus shown in Figure P13.27. Both velocity and temperature profiles are fully developed. The heat fluxes in from the two walls are different but are
Engine oil at a rate of \(0.05 \mathrm{~kg} / \mathrm{s}\) flows through a \(3 \mathrm{~mm}\) diameter tube that is \(30 \mathrm{~m}\) long. The oil has an inlet temperature of \(40^{\circ}
Water containing \(0.1 \mathrm{M}\) benzoic acid flows at \(0.1 \mathrm{~cm} / \mathrm{s}\) through a \(1 \mathrm{~cm}\) diameter rigid tube of cellulose acetate. The walls of the tube are \(0.01
Waste gases at a flowrate of \(15 \mathrm{~kg} / \mathrm{min}\) leave a plant through a chimney stack \(120 \mathrm{~m}\) high. The outer diameter of the chimney is \(1.5 \mathrm{~m}\) and the walls
We are interested in determining the Sherwood number in fully developed flow between parallel plates. The plates are formed from membranes that provide a constant mass flux into the fluid along their
Consider the same situation as in problem 13.31, but in this case one membrane provides a constant flux into the fluid while the other provides a flux of the same magnitude out of the fluid. What is
Consider the case of axial dispersion in steady, fully developed flow between stationary, parallel plates. The plates are of length, \(L\), and the separation distance between the plates is \(d\).
The dispersion model is often used to analyze the performance of non-ideal plug-flow reactors. In essence, the plug-flow reactor model is augmented by the addition of a diffusion-like term involving
Consider the dispersion model for the chemical reactor in the presence of a first-order chemical reaction, \(-r_{a}=k^{\prime \prime} c_{a}\).a. Write the steady-state model equation in dimensionless
Do turbulent boundary layers on a flat plate grow more slowly or faster than their laminar cousins?
Reynolds averaging leads to eddy transport coefficients. In isotropic turbulence, how many eddy viscosities are there and how are they related to one another?
The universal velocity profile splits the turbulent boundary layer into three distinct regions. What are they?
What are the critical Reynolds numbers for the transition from laminar to turbulent flow on a flat plate and within a tube?
The Dittus-Boelter and Sieder-Tate correlations are restricted to which types of tubes?
Turbulent flow over a sphere can lead to reduced drag coefficients, hence the dimples on a golf ball. Physically, what is it about the flow field that leads to smaller drag coefficients?
Two pipes are used to carry water between two open tanks whose water surfaces are at different elevations. One pipe has twice the diameter of the other. If both pipes have the same friction factor,
What characteristics of a spherical particle are required for its terminal velocity in air at \(25^{\circ} \mathrm{C}\) to just enter the turbulent regime, \(R e_{d}=R e_{d c}\) ?
A giant submarine needs to travel great distances to reach destinations. The submarine can be modeled as a cylinder with a radius of \(7 \mathrm{~m}\), a length of \(50 \mathrm{~m}\), and a weight of
A plane is flying at an altitude of 10,000 meters and a speed of \(810 \mathrm{~km} / \mathrm{hr}\). The fuselage of the plane can be considered a cylinder of diameter \(4 \mathrm{~m}\) and length
Water must be pumped from ground level to the top of a building. The building is \(30 \mathrm{~m}\) tall. We wish to compare the work required to pump water at three different average velocities: \(1
Water at \(350 \mathrm{~K}\) is flowing through a pipe at a flow rate of \(0.3 \mathrm{~kg} / \mathrm{s}\). The pipe is \(10 \mathrm{~mm}\) in diameter and has roughness,
A fluid flows along a flat, horizontal plate that is heated along its entire length. At a distance, \(x=10 \mathrm{~cm}\); from the leading edge of the plate the thermal boundary layer thickness,
Estimate the power required to overcome drag for a car traveling at \(100 \mathrm{~km} / \mathrm{hr}\). Typical car dimensions are \(3.5 \mathrm{~m} \times 1.7 \mathrm{~m} \times 1.5 \mathrm{~m}\)
The universal velocity profile in the turbulent core of smooth tubes was written as:\[U^{+}=2.5 \ln y^{+}+5.5\]This relationship holds when the friction Reynolds number is
Consider a rotating disk suspended in an infinite fluid. One remarkable result for laminar flow situations was that the boundary layer thickness and hence transport coefficients were uniform across
When pumping a fluid, the pressure at the entrance to the pump must never drop below the saturation pressure of the fluid. If the pressure does drop below the saturation pressure, cavitation (the
A sailboard is gliding across a lake at a speed of \(20 \mathrm{mph}(9 \mathrm{~m} / \mathrm{s})\). The sailboard is \(3 \mathrm{~m}\) long, \(0.75 \mathrm{~m}\) wide and represents a smooth, flat
Golf balls have had dimples in them for well over a century after it was first discovered that dimpled balls could be driven farther. Now we know that the dimples trip up the boundary layer and
Compare predictions of the Prandtl/von Karman universal resistance law and the Heng, Chan, Churchill/Zajic relation for the friction factor in smooth tube flow, equation (14.84).a. Plot the friction
In the late 1940s it was discovered that the addition of polymers that form random coiled structures in a fluid would reduce the power required to pump that fluid through a tube or to push an object
Consider a heat exchanger that has 1000, \(2.5 \mathrm{~cm}\) diameter smooth tubes in parallel, each \(6 \mathrm{~m}\) long. The total water flow of \(1 \mathrm{~m}^{3} / \mathrm{s}\) at
In the text we derived a formula for the friction factor based on the universal velocity profile. In essence it relates \(\sqrt{2 / C_{f}}=\bar{U}^{+}\). The universal velocity profile has a kink at
A new chemical plant requires a water flow rate of \(5.75 \mathrm{~m}^{3} / \mathrm{min}\). The gauge pressure in the water main, located in the street \(50 \mathrm{~m}\) from the plant, is \(800
For flow over a flat plate with an extremely rough surface, convection heat transfer effects are known to be correlated by the expression:\[N u_{x}=0.04 \operatorname{Re}_{x}^{0.9}
Water, initially at \(37^{\circ} \mathrm{C}\), is flowing through a cast iron pipe \(43 \mathrm{~mm}\) in diameter at a mass flow rate of \(10.1 \mathrm{~kg} / \mathrm{s}\). The tube is heated by
A very thin, lead \((\mathrm{Pb})\) wire of diameter \(\left(4 \times 10^{-5} \mathrm{~m}\right)\) and length \((1 \mathrm{~m})\) is placed in an air stream \(\left(1 \mathrm{~atm}, T_{\infty}=300
An insulated, thin walled tube, \(60 \mathrm{~m}\) long and \(25 \mathrm{~mm}\) inside diameter, is to deliver \(65^{\circ} \mathrm{C}\) hot water to a house. The water enters the tube at

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