New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
physics
fundamentals momentum heat

Fundamentals Of Momentum Heat And Mass Transfer 6th Edition James Welty, Gregory L. Rorrer, David G. Foster - Solutions

A source of strength 1.5 m2/s at the origin is combined with a uniform stream moving at 9 m/s in the x direction. For the half-body that results, finda. The stagnation pointb. The body height as it crosses the y axisc. The body height at large xd. The maximum surface
A line vortex of strength K at (x, y) (0, α) is combined with opposite strength vortex at (0, α). Plot the streamline pattern and find the velocity that each vortex induces on the other vortex.
The stream function for an in-compressible, two dimensional flow field is ψ = 3x2y + y For this flow field, sketch several streamlines.
Sketch the streamlines and potential lines of the flow due to a line source of at (a, 0) plus an equivalent sink at (a, 0).
Calculate the total lift force on the Arctic hut shown below as a function of the location of the opening. The lift force results from the difference between the inside pressure and the outside pressure. Assume potential flow, and that the hut is in the shape of a half-cylinder. Opening ө |
Determine the pressure gradient at the stagnation point of Problem 10.10(a).Data From Problem 10.10(a)For the velocity potentials given below, find the stream function and sketch the streamlines a. Зху?] 3 Ф%3D, 3.
In Problem 10.12, how far upstream does the flow from the source reach?Data From Problem 10.12For the case of a source at the origin with a uniform free stream plot the streamline ψ = 0.
For the case of a source at the origin with a uniform free stream plot the streamline ψ = 0.
The stream function for an in-compressible, two dimensional flow field is ψ = 2r3 sin 3θFor this flow field, plot several streamlines for 0 ≤ θ ≤ π/3.
Consider the process shown in the figure. A bulk gas stream containing 0.10 mole% of carbon monoxide (CO) gas, 2.0 mole% O2gas, and 97.9 mole% of CO2gas flows over a flat catalytic surface of length 0.50 m at a bulk velocity of 40 m/s at 1.0 atm and 600 K. Heat-transfer processes maintain the gas
For the velocity potentials given below, find the stream function and sketch the streamlines a. b.c. Зху?] 3 Ф%3D, 3. ху Ф — 0
At what point on the surface of the circular cylinder in a potential flow does the pressure equal the free-stream pressure?
In Problem 10.7, explain how one could obtain ∂vθ /∂θ at the stagnation point, using only r and ∂vr /∂r.Data From Problem 10.7For the flow about a cylinder, find the velocity variation along the streamline leading to the stagnation point. What is the velocity derivative ∂vr/∂r at the
For the flow about a cylinder, find the velocity variation along the streamline leading to the stagnation point. What is the velocity derivative ∂vr/∂r at the stagnation point?
Make an analytical model of a tornado using an irrotational vortex (with velocity inversely proportional to distance from the center) outside a central core (with velocity directly proportional to distance). Assume that the core diameter is 200 ft and the static pressure at the center of the core
The velocity potential for a given two-dimensional flow field is ϕ = (5/3) x3 - 5xy2Show that the continuity equation is satisfied and determine the corresponding stream function.
In polar coordinates, the continuity equation for steady in-compressible flow becomes Derive equations (10-10), using this relation. 1 dve = 0 r д0 : (rv,) + - r дr 1 д Ur Ә Vө r д0 дr
Find the stream function for a flow with a uniform free stream velocity v∞.The free-stream velocity intersects the x axis at an angle α.
Determine the fluid rotation at a point in polar coordinates, using the method illustrated in Figure 10.1. УА B B Ду t + At Дr х
In polar coordinates, show that 1 ГО(rv) ди; ez дө Уху- дr
Consider steady, continuous, in-compressible, fully developed laminar flow of a Newtonian fluid in an infinitely long round pipe of diameter D inclined at an angle a. The fluid is not open to the atmosphere and flows down the pipe due to an applied pressure gradient and from gravity. Derive an
A wide moving belt passes through a container of a viscous liquid. The belt moves vertically upward with constant velocity vw, as illustrated in the figure. Because of viscous forces, the belt picks up a thin film of fluid having a thickness h. Use the appropriate form of the Navierâ€“Stokes
Two immiscible fluids are flowing down between two flat, infinitely long flat parallel plates as shown in the figure below. The plate on the left is moving down with a velocity of vA, and the plate on the right is moving up with a velocity vB. The dotted line is the interface between the two
Beginning with the appropriate form of the Navier€“ Stokes equations, develop an equation in the appropriate coordinate system to describe the velocity of a fluid that is flowing in the annular space as shown in the figure. The fluid is Newtonian, and is flowing in steady,
Determine the velocity profile in a fluid situated between two coaxial rotating cylinders. Let the inner cylinder have radius R1, and angular velocity Ω1; let the outer cylinder have radius R2 and angular velocity Ω2.
For the flow described in Problem 8.13, obtain the differential equation of motion if vθ = f(r, t).
Using the Navier–Stokes equations in Appendix E, solve Problem 8.13.
Using the Navier–Stokes equations, find the differential equation for a radial flow in which vz = vθ = 0, and vr = f (r). Using continuity, show that the solution to the equation does not involve viscosity.
Using the Navier–Stokes equations as given in Appendix E, work Problems 8.17 and 8.18.
Obtain the equations for one-dimensional inviscid, unsteady, compressible flow.
Obtain the equations for a one-dimensional steady, viscous, compressible flow in the x direction from the Navier– Stokes equations. (These equations, together with an equation of state and the energy equation, may be solved for the case of weak shock waves.)
Using the laws for the addition of vectors and equation (9-19), show that in the absence of gravity,a. The fluid acceleration, pressure force, and viscous force all lie in the same planeb. In the absence of viscous forces the fluid accelerates in the direction of decreasing pressurec. A static
In polar coordinates, the continuity equation isShow thata. if vÎ¸ = 0, then vr = F(Î¸)/rb. if vr = 0, then vÎ¸ = f(r) |1 д 1 дуд (rv,) +- r д0 гдr
Derive equation (2-3) from equation (9-27). Dv = pg – VP Dt
Write equations (9-17) in component form for Cartesian coordinates. ду +V. (μV υ.) дх + V. OP Dvx = P8x P Dt Əx
In a velocity field where v = 400[(y/L)2ex + (x/L)2ey] fps, determine the pressure gradient at the point (L, 2L). The y axis is vertical, the density is 64.4 Ibm/ft3 and the flow may be considered inviscid.
The atmospheric density may be approximated by the relation ρ = ρ0 exp(-y/β), where β = 22,000 ft. Determine the rate at which the density changes with respect to body falling at v fps. If v = 20,000 fps at 100,000 ft, evaluate the rate of density change.
Does the velocity distribution in Example 2 satisfy continuity?
Using the Navier€“Stokes equations and the continuity equation, obtain an expression for the velocity profile between two flat, parallel plates.Continuity equation, дv0 ду дих дх
For flow at very low speeds and with large viscosity (the so-called creeping flows) such as occur in lubrication, it is possible to delete the inertia terms, Dv/Dt from the Navier- Stokes equation. For flows at high velocity and small viscosity, it is not proper to delete the viscous term v∇2 v.
Find Dv/Dt in polar coordinates by taking the derivative of the velocity. (v = vr (r, θ, t)er + vθ (r, θ, t)eθ. Remember that the unit vectors have derivatives.)
In an in-compressible flow, the volume of the fluid is constant. Using the continuity equation, ∇ • v = 0, show that the fluid volume change is zero.
In Cartesian coordinates, show thatmay be written (v €¢ ˆ‡). What is the physical meaning of the term (v €¢ ˆ‡)? д д д + Vz д ду dy дх
Apply the law of conservation of mass to an element in a polar coordinate system and obtain the continuity equation for a steady, two-dimensional, in-compressible flow.
You have been asked to calculate the density of an in-compressible Newtonian fluid in steady flow that is flowing continuously at 250°F along a 2500-ft pipe with a constant diameter of 4 in. and a volumetric flow rate of 2.5 ft3/s. The only fluid properties known are the kinematic viscosity, -7.14
Benzene, which is an in-compressible Newtonian fluid, flows steadily and continuously at 150°F through a 3000-ft pipe with a constant diameter of 4 in. with a volumetric flow rate of 3.5 ft3/s. Assuming fully developed laminar flow, and that the no-slip boundary condition applies, calculate the
A Newtonian fluid in continuous, in-compressible laminar flow is moving steadily through a very long 700-m, horizontal pipe. The inside radius is 0.25 m for the entire length, and the pressure drop across the pipe is 1000 Pa. The average velocity of the fluid is 0.5 m/s. What is the viscosity of
Benzene flows steadily and continuously at 100°F through a 3000-ft horizontal pipe with a constant diameter of 4 in. The pressure drop across the pipe under these conditions is 300 lbf/ft2. Assuming fully developed, laminar, in-compressible flow, calculate the volumetric flow rate and average
Determine the maximum film velocity in Problem 8-15.Data From Problem 8.15A viscous film drains uniformly down the side of a vertical rod of radius R. At some distance down the rod, the film approaches a terminal or fully developed flow such that the film thickness, h, is constant and vz = f (r).
A viscous film drains uniformly down the side of a vertical rod of radius R. At some distance down the rod, the film approaches a terminal or fully developed flow such that the film thickness, h, is constant and vz = f (r). Neglecting the shear resistance due to the atmosphere, determine the
Oil is supplied at the center of two long plates. The volumetric flow rate per unit length is Q and the plates remain a constant distance, b, apart. Determine the vertical force per unit length as a function of the Q, μ, L, and b.
The device in the schematic diagram on the next page is a viscosity pump. It consists of a rotating drum inside of a stationary case. The case and the drum are concentric. Fluid enters at A, flows through the annulus between the case and the drum, and leaves at B. The pressure at B is higher than
A continuous belt passes upward through a chemical bath at velocity v0 and picks up a film of liquid of thickness h, density, ρ, and viscosity μ. Gravity tends to make the liquid drain down, but the movement of the belt keeps the fluid from running off completely. Assume that the flow is a well
Derive the equation of motion for a one-dimensional, inviscid, unsteady compressible flow in a pipe of constant cross sectional area neglect gravity.
Fluid flows between two parallel plates, a distance h apart. The upper plate moves at velocity, v0; the lower plate is stationary. For what value of pressure gradient will the shear stress at the lower wall be zero?
Determine the velocity profile for fluid flowing between two parallel plates separated by a distance 2h. The pressure drop is constant.
Two immiscible fluids of different density and viscosity are flowing between two parallel plates. Express the boundary conditions at the interface between the two fluids.
The viscosity of heavy liquids, such as oils, is frequently measured with a device that consists of a rotating cylinder inside a large cylinder. The annular region between these cylinders is filled with liquid and the torque required to rotate the inner cylinder at constant speed is computed, a
A thin rod of diameter d is pulled at constant velocity through a pipe of diameter D. If the wire is at the center of the pipe, find the drag per unit length of wire. The fluid filling the space between the rod and the inner pipe wall has density ρ and viscosity μ.
Derive the expressions for the velocity distribution and for the pressure drop for a Newtonian fluid in fully developed laminar flow in the annular space between two horizontal, concentric pipes. Apply the momentum theorem to an annular fluid shell of thickness Î”r and show that the
A common type of viscosimeter for liquids consists of a relatively large reservoir with a very slender outlet tube, the rate of outflow being determined by timing the fall in the surface level. If oil of constant density flows out of the viscosimeter shown at the rate of 0.273 cm3/s, what is the
A 0.635-cm hydraulic line suddenly ruptures 8 m from a reservoir with a gage pressure of 207 kPa. Compare the laminar and inviscid flow rates from the ruptured line in cubic meters per second.
A 40-km-long pipeline delivers petroleum at a rate of 4000 barrels per day. The resulting pressure drop is 3.45 × 106 Pa. If a parallel line of the same size is laid along the last 18 km of the line, what will be the new capacity of this network? Flow in both cases is laminar and the pressure drop
Express equation (8-9) in terms of the flow rate and the pipe diameter. If the pipe diameter is doubled at constant pressure drop, what percentage change will occur in the flow rate?Equation (8-9) 8μυν -32 μυνg R2 Ξ D2 dx
The figure below shows the geometry of a rheological experiment. A fluid lies between R0and Ri, where Ri= 16.00 mm and R0= 17.00 mm. The gap between the two cylinders can be modeled as two parallel plates separated by a fluid. The inner cylinder is rotated at 6000 rpm, and the torque is measured to
A thin coating is to be applied to both sides of a piece of thin plastic that is being mechanically transported. The plastic is 4.5- µm-thick and 0.0254-meters-wide and is very long. We want to coat a specific length of the plastic that is 1 meter in length. This thin plastic will break if the
A Newtonian oil with a density of 60 lbm/ft3, viscosity of 0.206 Ã— 10-3Ibm/ft-s and kinematic viscosity of 0.342 Ã— 10-5ft2/s undergoes steady shear between a horizontal fixed lower plate and a moving horizontal upper plate. The upper plate is moving with a velocity of 3
The rate of shear work per unit volume is given by the product τv. For a parabolic velocity profile in a circular tube (see Example 4.2), determine the distance from the wall at which the shear work is maximum.
What pressure drop per foot of tube is caused by the shear stress in Problem 7.17?Data From Problem 7.17For water flowing in a 0.1-in.-diameter tube, the velocity distribution is parabolic (see Example 4.2). If the average velocity is 2 fps, determine the magnitude of the shear stress at the tube
For water flowing in a 0.1-in.-diameter tube, the velocity distribution is parabolic (see Example 4.2). If the average velocity is 2 fps, determine the magnitude of the shear stress at the tube wall.
The conical pivot shown in the figure has angular velocity Ï‰ and rests on an oil film of uniform thickness h. Determine the frictional moment as a function of the angle Î±, the viscosity, the angular velocity, the gap distance, and the shaft diameter. -D- y. -2a
A cross-flow molecular filtration device equipped with a mesoporous membrane is used to separate the enzyme lysozyme from a fermentation broth, as shown in the figure (right column). Water at 25°C flows over the top surface of the flat plate membrane at a velocity of 5.0 cm/s. The length of the
If the ram and auto rack in the previous problem together have a mass of 680 kg, estimate the maximum sinking speed of the ram and rack when gravity and viscous friction are the only forces acting. Assume 2.44 m of the ram is engaged.
An auto lift consists of 36.02-cm-diameter ram that slides in a 36.04-cm-diameter cylinder. The annular region is filled with oil having a kinematic viscosity of 0.00037 m2/s and a specific gravity of 0.85. If the rate of travel of the ram is 0.15 m/s, estimate the frictional resistance when 3.14 m
Two ships are traveling parallel to each other and are connected by flexible hoses. Fluid is transferred from one ship to the other for processing and then returned. If the fluid is flowing at 100 kg/s, and at a given instant the first ship is making 4 m/s whereas the second ship is making 3.1 m/s,
Gasoline from an under-storage storage tank leaked down onto an impermeable clay barrier and collected into a liquid pool. A simplified picture of the situation is provided in the figure below. Directly over this underground pool of liquid gasoline (ii-octane, species A) is a layer of gravel of 1.0
If the speed of the shaft is doubled in Problem 7.11, what will be the percentage increase in the heat transferred from the bearing? Assume that the bearing remains at constant temperature.
A flat steel plate of 2.0 m length and 2.0 m width initially contains a very thin coating of light hydrocarbon lubricating oil (species A) used in a manufacturing process. An engineer is considering the feasibility of using hot forced air convection to remove the lubricating oil from the surface as
An automobile crankshaft is 3.175 cm in diameter. A bearing on the shaft is 3.183 cm in diameter and 2.8 cm long. The bearing is lubricated with SAE 30 oil at a temperature of 365 K. Assuming that the shaft is centrally located in the bearing, determine how much heat must be removed to maintain the
Repeat the preceding problem for air.Data From Problem 7.9According to the Hagen–Poiseuille laminar flow model, the volumetric flow rate is inversely proportional to the viscosity. What percentage change in volumetric flow rate occurs in a laminar flow as the water temperature changes from near
A well-mixed open pond contains wastewater that is contaminated with a dilute concentration of dissolved methylene chloride. The pond is rectangular with dimensions of 500 m by 100 m, as shown in the figure (above right). Air at 27°C and 1.0 atm blows parallel to the surface of the pond with a
According to the Hagen–Poiseuille laminar flow model, the volumetric flow rate is inversely proportional to the viscosity. What percentage change in volumetric flow rate occurs in a laminar flow as the water temperature changes from near freezing to 140°F?
At what temperature is the kinematic viscosity of glycerin the same as the kinematic viscosity of helium?
What is the percentage change in the viscosity of water when the water temperature rises from 60 to 120°F?
Calculate the viscosity of oxygen at 350 K and compare with the value given in Appendix I.
Estimate the viscosity of nitrogen at 175 K using equation (7-10). 28 · 183 1.200 · 10- µ = 2.6693 · 10-6. Pa · s (3.681)²(1.175)
Using a cylindrical element, show that Stokes€™s viscosity relation yields the following shear stress components: 1д0- Trо— Төr — и|r- дr rдө 1д0. дvв + поб) д. Теz — Tz0 —и rд0 Гдu, Tzr = Trz = µ [ər до дz
Show that the axial strain rate in a one-dimensional flow, vx = vx (x), is given by ∂vx/∂x. What is the rate of volume change? Generalize for a three-dimensional element, and determine the rate of volume change.
For a two-dimensional, in-compressible flow with velocity vx = vx(y), sketch a three-dimensional fluid element and illustrate the magnitude, direction, and surface of action of each stress component.
Sketch the deformation of a fluid element for the following cases:a. ∂vx/∂y is much larger than ∂vy/∂xb. ∂vy/∂x is much larger than ∂vx/∂y
In the development of the approximate solution for solving the laminar concentration boundary layer formed by fluid flow over a flat plate, it is necessary to assume a concentration profile. Equation (28-35a) was obtained by analysis of a power-series concentration profile of the form cA
You have been asked to do an analysis of a pump that will transfer a fluid. The inlet to a pump has a diameter of 0.35 m, and the pressure to the pump is 2500 kg/m-s2. The outlet from the pump has a diameter of 0.15 m and a pressure of 6000 kg/m-s2. The fluid being pumped has a viscosity of 1.09 ×
Air flows steadily through a turbine that produces 3.5 105ft-lbf/s of work. Using the data below at the inlet and outlet, where the inlet is 10 feet below the outlet, please calculate the heat transferred in units of BTU/hr. You may assume steady flow and ignore viscous work. Inlet Outlet diameter
You have been asked to do an analysis of a steady state pump that will transfer Aniline, an organic material, from one area to another in a chemical plant. Please determine the temperature change that the fluid undergoes during this process. The flow rate is constant in the system at 1.0 ft3/sec.
In using the von KÃ¡rmÃ¡n approximate method for analyzing the turbulent boundary layer over a flat plate, the following velocity and concentration profiles were assumed:andThe four constants€“Î±, Î², Î·, and Î¶
Butyl alcohol, a Newtonian fluid, is being pumped at steady state with the density of 50 Ibm/ft3. viscosity of 1.80 × 10-3 Ibm/ft s, heat capacity of 0.58 Btu/lbm °F, and kinematic viscosity of 3.60 × 10-5 ft2/s. The inlet to the pump is a pipe with a diameter of 6 in., and
A client has asked you to find the pressure change in a pumping station. The outlet from the pump is 20 ft above the inlet. A Newtonian fluid is being pumped at steady state. At the inlet to the pump where the diameter is 6 in., the temperature of the fluid is 80°F, the viscosity is 1.80 × 10-3
The tank in the previous problem feeds two lines, a 4-cm pipe that exits 10 m below the water level in the tank and a second line, also 4 cm in diameter runs from the tank to a station 20 m below the water level in the tank. The exits of both lines are open to the atmosphere. Assuming friction less
Consider a 4-cm pipe that runs between a tank open to the atmosphere and a station open to the atmosphere 10 m below the water surface in the tank. Assuming friction less flow, what will be the mass flow rate? If a nozzle with a 1-cm diameter is placed at the pipe exit, what will be the mass flow
Repeat the previous problem without the assumption that the velocity in the heating section is negligible. The ratio of the flow area of the heating section to the chimney flow area is R.Data From Problem 6.35A fluid of density Ï1 enters a chamber where the fluid is heated so that the

Showing 700 - 800 of 972

1
2
3
4
5
6
7
8
9
10

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved