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physics
fundamentals momentum heat
Fundamentals Of Momentum Heat And Mass Transfer 6th Edition James Welty, Gregory L. Rorrer, David G. Foster - Solutions
What is the pressure difference between points A and B if d1= 1.7 ft, d2= 1 in., and d3= 6.3 in.? d2 Н.о d1 Hg dз H20
Find the difference in pressure between tanks A and B, if d1= 2 ft, d2= 6 in., d3= 2.4 in., and d4= 4 in. Air. B da 45° H20 Hg dz A d1 d2
What is the pressure pAin the figure? The specific gravity of the oil is 0.8. PA Air Open Oil 10' 15' H20 1' Hg
Using a liquid having a specific gravity of 1.2 and inverting a tube full of this material as shown in the figure, what is the value of h if the vapor pressure of the liquid is 3 psia? h
Find the pressure at point A. Kerosene Water temp. = 150°F • Mercury in.→ RRAAA →15 in.
Determine the depth change to cause a pressure increase of 1 atm for (a) water, (b) sea water (SG = 1.0250), and (c) mercury (SG = 13.6).
The deepest known point in the ocean is 11,034 m in the Mariana Trench in the Pacific. Assuming sea water to have a constant density of 1050 kg/m3, determine the pressure at this point in atmospheres.
Matter is attracted to the center of Earth with a force proportional to the radial distance from the center. Using the known value of g at the surface where the radius is 6330 km, compute the pressure at Earth’s center, assuming the material behaves like a liquid, and that the mean specific
The practical depth limit for a suited diver is about 185 m. What is the gage pressure in sea water at that depth? The specific gravity of sea water is 1.025.
The change in density due to temperature causes the takeoff and landing speeds of a heavier-than-air craft to increase as the square root of the temperature. What effect do temperature induced density changes have on the lifting power of a rigid lighter-than-air craft?
If the density of sea water is approximated by the equation of state p = p0 exp[(p - patm)/β], where β is the compressibility, determine the pressure and density at a point 32,000 ft below the surface of the sea. Assume β = 30,000 psi.
In Problem 2.2, find the depth at which the net force on the tank is zero. Data From Problem 2.2 The open end of a cylindrical tank 2 ft in diameter and 3 ft high is submerged in water as shown. If the tank weights 250 lb, to what depth h will the tank submerge? The air barometric pressure is 14.7
The open end of a cylindrical tank 2 ft in diameter and 3 ft high is submerged in water as shown. If the tank weights 250 lb, to what depth h will the tank submerge? The air barometric pressure is 14.7 psia. The thickness of tank wall may be neglected. What additional force is required to bring the
A thin polymer film contains some residual solvent. It is desired to evaporate the volatile solvent (n-hexane, solute A) from the polymer using the process shown in the figure below. The wet polymer film enters the drying process. Both the top and bottom surfaces of the polymer film are exposed to
On a certain day the barometric pressure at sea level is 30.1 in. Hg, and the temperature is 70°F. The pressure gage in an airplane in flight indicates a pressure of 10.6 psia, and the temperature gage shows the air temperature to be 46°F. Estimate as accurately as possible the altitude of the
A beaker of water with a density of 987 kg / m3 has a capillary tube inserted into it. The water is rising in the capillary tube to a height of 1.88 cm. The capillary tube is very clean and has a diameter of 1.5 mm. What is the temperature of the water?
A colleague is trying to measure the diameter of a capillary tube, something that is very difficult to physically accomplish. Since you are a Fluid Dynamics student, you know that the diameter can be easily calculated after doing a simple experiment. You take a clean glass capillary tube and place
An experimental fluid is used to create a spherical bubble with a diameter of 0.25 cm. When in contact with a surface made of plastic, it has a contact angle of 30 degrees. The pressure inside the bubble is 101453 Pa and outside the bubble the pressure is atmospheric. In a particular experiment,
Determine the diameter of the glass tube necessary to keep the capillary-height change of water at 30°C less than 1 mm.
At 60°C the surface tension of water is 0.0662 N/m and that of mercury is 0.47 N/m. Determine the capillary height changes in these two fluids when they are in contact with air in a glass tube of diameter 0.55 mm. Contact angles are 0° for water and 130° for mercury.
An open, clean glass tube, having a diameter of 3 mm, is inserted vertically into a dish of mercury at 20°C. Determine how far the column of mercury in the tube will be depressed for a contact angle of 130°.
Determine the difference in pressure between the inside and outside of a soap film bubble at 20°C if the diameter of the bubble is 4 mm.
Determine the height to which water at 68°C will rise in a clean capillary tube having a diameter of 0.2875 cm.
Using the expression for the gradient in polar coordinates (Appendix A), find the gradient of ψ (r, θ) whenWhere is the gradient maximum? The terms A and a are constant. a² V = Ar sin 0( 1
If the fluid of density p in Problem 1.3 obeys the perfect gas law, obtain the equation of state of the mixture€”that is, P = f (ps, (RT/M) , pm, x). Will this result be valid if a liquid is present instead of a solid?Data From Problem 1.3For a fluid of density p in which solid particles
A scalar field is given by the function ∅ = 3x2y + 4y2.a. Find ∇ ∅ at the point (3, 5).b. Find the component of ∇ ∅ that makes a - 60° angle with the x axis at the point (3, 5).
Are the fields described in Problems 1.11 and 1.12 dimensionally homogeneous? What must the units of pˆžbe in order that the pressure be in pounds per square foot when vˆžis given in feet per second (Problem 1.11)?Data From Problem 1.11Find the pressure gradient at point (a,b)
Find the temperature gradient at point (a, b) at time t = (L2/a) ln e when the temperature field is given bywhere T0, a, a, and b are constants. T = Toe-at/4L' sin * cosh: y a
Find the pressure gradient at point (a,b) when the pressure field is given by where pˆž, vˆž, a, and b are constants. P = P,V (sin - sin + 2 х y ал a.
Transform the operator ˆ‡ to cylindrical coordinates (r, θ, z), using the results of Problems 1.7 and 1.9.Data From Problem 1.7Show that the unit vectors er and eθ in a cylindrical coordinate system are related to the unit vectors ex and ey byer = ex cos
Using the geometric relations given below and the chain rule for differentiation, show thatandwhen r2 = x2 + y2 and tanθ = y/x. sin 0 д д д + cos 0. дr r д0 дх д cos 0 a r д0 д + sin 0 дr ду ||
Using the results of Problem 1.7, show that der/dθ = eθ and deθ/dθ = -er.Data From Problem 1.7Show that the unit vectors er and eθ in a cylindrical coordinate system are related to the unit vectors ex and ey byer = ex cos θ + ey sin θandeθ = -ex sin θ + ey cos θ
Show that the unit vectors er and eθ in a cylindrical coordinate system are related to the unit vectors ex and ey byer = ex cos θ + ey sin θandeθ = -ex sin θ + ey cos θ
Using the information given in Problem 1.1 and the properties of the standard atmosphere given in Appendix G, estimate the number of molecules per cubic inch at an altitude of 250,000 ft.Data From Problem 1.1The number of molecules crossing a unit area per unit time in one direction is given
What pressure change is required to change the density of air by 10% under standard conditions?
An equation linking water density and pressure iswhere the pressure is in atmospheres and B = 3000 atm. Determine the pressure in psi required to increase water density by 1% above its nominal value. P+B P1 + B P1,
For a fluid of density p in which solid particles of density psare uniformly dispersed, show that if x is the mass fraction of solid in the mixture, the density is given by PsP Pmixture px + p,(1 – x)
An investigator proposes to study the mass-transfer process for the dissolution of a single solid sphere suspended within a turbulent flow stream. Predict the variables that would be used to explain the geometry involved, the properties of the moving stream, and the convective mass-transfer
Which of the quantities listed below are flow properties and which are fluid properties?pressure temperature velocitydensity stress
Define the Stanton and Peclet numbers and their relationships to other dimensionless groups for convection mass transfer.
The number of molecules crossing a unit area per unit time in one direction is given bywhere n is the number of molecules per unit volume and v is the average molecular velocity. As the average molecular velocity is approximately equal to the speed of sound in a perfect gas, estimate the number of
Determine the capillary rise for a water-air-glass interface at 40°C in a clean glass tube having a radius of 1 mm.
A glass tube having an inside diameter of 0.25 mm and an outside diameter of 0.35 mm is inserted into a pool of mercury at 20°C such that the contact angle is 130°. Determine the upward force on the glass.
Two clean and parallel glass plates, separated by a gap of 1.625 mm, are dipped in water. If σ = 0.0735 N/m, determine how high the water will rise.
Water in a container is originally at 100 kPa. The water is subjected to a pressure of 120 MPa. Determine the percentage decrease in its volume.
The bulk modulus of elasticity for water is 2.205 GPa. Determine the change in pressure required to reduce a given volume by 0.75%.
A pressure of 10 MPa is applied to 0.25 m3 of a liquid, causing a volume reduction of 0.005 cm3. Determine the bulk modulus of elasticity.
A liquid in a cylinder has a volume of 1200 cm3 at 1.25MPa and a volume of 1188 cm3 at 2.50 MPa. Determine its bulk modulus of elasticity.
A vertical cylindrical tank having a base diameter of 10 m and a height of 5 m is filled to the top with water at 20°C. How much water will overflow if the water is heated to 80°C?
Given the following expression for the pressure field where x, y, and z are space coordinates, t is time, and P0, p, Vˆž, and L are constants. Find the pressure gradient Vot 2 P = Po +pV% хуZ +3 L3
The determination of the boundary-layer thickness is important in many applications. For the case of aniline at 100°F, flowing at a rate of 2 ft/s along a flat plate, what will be the thickness of the boundary layer at a position 0.1 ft beyond the leading edge?
The velocity vector in a two-dimensional flow is given by the expression v = 10ex + 7xey m/s when x is measured in meters. Determine the component of the velocity that makes a -30° angle with the x axis at the point (2, 2).
Water is flowing through a large circular conduit with a velocity profile given by the equation v = 9(1 - r2 /16) fps. What is the average water velocity in the 1.5-ft pipe? 8 ft d = 1.5 ft
Water enters a 4-in. square channel as shown at a velocity of 10 fps. The channel converges to a 2-in. square configuration as shown at the discharge end. The outlet section is cut at 30° to the vertical as shown, but the mean velocity of the discharging water remains horizontal. Find the
Water enters one end of a perforated pipe 0.2 m in diameter with a velocity of 6 m/s. The discharge through the pipe wall is approximated by a linear profile. If the flow is steady, find the discharge velocity. 0.5 m 6 m/s 2 미2
Salt water containing 1.92 lb/gal of salt flows at a fixed rate of 2 gal/min into a 100-gal tank, initially filled with fresh water. The density of the incoming solution is 71.8 lb/ft3. The solution, kept uniform by stirring, flows out at a fixed rate of 19.2 lb/min.a. How many pounds of salt will
In the piston and cylinder arrangement shown below, the large piston has a velocity of 2 fps and an acceleration of 5 fps2. Determine the velocity and acceleration of the smaller piston. 2 fps 5 fps? d = 4 in. d = 0.5 in. Oil
Show that in a one-dimensional steady flow the following equation is valid:dA / A + dv / v + dρ / ρ = 0
Using the symbol M for the mass in the control volume, show that equation (4-1) may be written ƏM dm= 0 C.S. +
A shock wave moves down a pipe as shown below. The fluid properties change across the shock, but they are not functions of time. The velocity of the shock is vw. Write the continuity equation and obtain the relation between p2, p1, v2, and vw. The mass in the control volume at any time is M = p2Ax
In the figure below, the x-direction velocity profiles are shown for a control volume surrounding a cylinder. If the flow is in-compressible, what must the rate of flow be across the horizontal control-volume surface? Ux = Vo 6d vo Ux = v0
Two very long parallel plates of length 2L are separated a distance b. The upper plate moves downward at a constant rate V. A fluid fills the space between the plates. Fluid is squeezed out between the plates. Determine the mass flow rate and maximum velocity under the following
A thin layer of liquid, draining from an inclined plane, has a velocity profile vx‰ˆ v0 (2y/h - y2/h2), where v0is the surface velocity. If the plane has width 10 cm into the paper, determine the volume rate of flow in the film. Suppose that h = 2 cm and the flow rate is 2 L/min.
The V-shaped tank has width w into the paper and is filled from the inlet pipe at volume flow Q. Derive expressions for (a) the rate of change dh/dt and (b) the time required for the surface to rise from h1to h2. 20° 20°
Water flows steadily through the piping junction, entering section 1 at 0.0013 m3/s. The average velocity at section 2 is 2.1 m/s. A portion of the flow is diverted through the shower head, which contains 100 holes of 1-mm diameter. Assuming uniform shower flow, estimate the exit velocity from the
The jet pump injects water at V1= 40 m/s through a 7.6 cm pipe and entrains a secondary flow of water V2= 3 m/s in the annular region around the small pipe. The two flows become fully mixed downstream, where V3is approximately constant. For steady in-compressible flow, compute V3. 7.6 cm |V2 V3 V1
A vertical, cylindrical tank closed at the bottom is partially filled with an in-compressible liquid. A cylindrical rod of diameter di (less than tank diameter, d0) is lowered into the liquid at a velocity V. Determine the average velocity of the fluid escaping between the rod and the tank walls
The hypodermic needle shown below contains a liquid serum (p = 1 g/cm3). If the serum is to be injected steadily at 6 cm3/s, how fast should the plunger be advanced (a) if leakage in the plunger clearance is neglected and (b) if leakage is 10% of the needle flow? 0.8 mm 2 cm
In-compressible steady flow in the inlet between parallel plates is uniform, V0= 8 cm/s, while downstream, the flow develops into the parabolic profile vx= az(z0- z), where a is a constant. What is the maximum value of vx? AZ Vo Zo
You are going to pressurize a tube using a mechanical pump. The standard bicycle tube is wrapped around a 24-in. diameter metal rim. The inflow to the pump is constant at 1 ft3/min. The density of the air leaving the pump is 0.075 lbm/ft3. The final inflated volume of a bicycle tube is 0.6 ft3. The
A large tank of unknown total volume is initially filled with 6000 g of a 10% by mass sodium sulfate solution. Into this tank a 50% sodium sulfate solution is added at a rate of 40 g/min. At the single outlet to the tank flows a 20 g/L solution at a rate of 0.01667 L/sec. Please calculate (a)
A cylindrical water tank is 4 feet high, with a 3-foot diameter, open to the atmosphere at the top is initially filled with water with a temperature of 60°F. The outlet at the bottom with a diameter of 0.5 in. is opened and the tank empties. The average velocity of the water exiting the tank is
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