Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 1, Problem 1.21P
Aeronautical engineers measure the pitching moment M0 of a wing and then write it in the following form for vise in other cases:
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
HW-1-.docx
->
Q1/ complete the dimensional formula and SI units for table.
US
Physical
Quantity
SI. No
Dimensional Formula
S.I Unit
customary
unit
Area (A)
work (w)
3
Density (d)
4
Speed (s)
stress (6)
Acceleration
(a)
Q2/ Suppose we are told that the acceleration a of a particle moving with uniform
speed v in a circle of radius r is proportional to some power of r, say r", and some
power of v, say vm , also some power of mass, say m". Determine the values of n
and m and o
Q3/ Show that the expression (x, = x +v, t+ % a t) is dimensionally correct, where
X, and x, are the position and a is the acceleration, and t is the time, v is the
velocity.
Thermal conductivity k is a measure of the ability of a material to conduct heat. For conduction heat transfer in the x-direction through a surface normal to the x-direction, Fourier’s law of heat conduction is expressed as: Q=-kA.dT/dx
where ?̇ is the rate of heat transfer and A is the area normal to the direction of heat transfer. Determine the primary dimensions of thermal conductivity (k). Look up a value of k and verify that its SI units are consistent with your result. Write a set of primary SI units for k.
Units and dimensions are important in any engineering analysis. This problem is about that.
In an old heat transfer textbook, you found the following equation for some specific heat transfer problem.
Ə²T Q
+
əx² λ
ƏT
Ət
You know that T is temperature (K) and x is the x-coordinate,
which is measured in meters. You also know that t is time (s) and the book uses as the symbol for
thermal conductivity, whose unit is W/m.K. What must be the units of Q and B?
Chapter 1 Solutions
Fluid Mechanics
Ch. 1 - Prob. 1.1PCh. 1 - Table A.6 lists the density of the standard...Ch. 1 - For the triangular element in Fig, P1.3,show that...Ch. 1 - Sand, and other granular materials, appear to...Ch. 1 - The mean free path of a gas, l, is defined as the...Ch. 1 - Henri Darcy, a French engineer, proposed that the...Ch. 1 - Convert the following inappropriate quantities...Ch. 1 - Suppose we know little about the strength of...Ch. 1 - A hemispherical container, 26 inches in diameter,...Ch. 1 - The Stokes-Oseen formula [33] for drag force F on...
Ch. 1 - P1.11 In English Engineering units, the specific...Ch. 1 - For low-speed (laminar) steady flow through a...Ch. 1 - The efficiency ? of a pump is defined as the...Ch. 1 - Figure P1.14 shows the flow of water over a dam....Ch. 1 - The height H that fluid rises in a liquid...Ch. 1 - Algebraic equations such as Bernoulli's relation,...Ch. 1 - The Hazen-Williams hydraulics formula for volume...Ch. 1 - For small particles at low velocities, the first...Ch. 1 - In his study of the circular hydraulic jump formed...Ch. 1 - Books on porous media and atomization claim that...Ch. 1 - Aeronautical engineers measure the pitching moment...Ch. 1 - Prob. 1.22PCh. 1 - During World War II, Sir Geoffrey Taylor, a...Ch. 1 - Air, assumed to be an ideal gas with k = 1.40,...Ch. 1 - On a summer day in Narragansett, Rhode Island, the...Ch. 1 - When we in the United States say a car's tire is...Ch. 1 - Prob. 1.27PCh. 1 - Wet atmospheric air at 100 percent relative...Ch. 1 - Prob. 1.29PCh. 1 - P1.30 Repeat Prob. 1.29 if the tank is filled with...Ch. 1 - Prob. 1.31PCh. 1 - Prob. 1.32PCh. 1 - A tank contai as 9 kg of CO2at 20°C and 2.0 MPa....Ch. 1 - Consider steam at the following state near the...Ch. 1 - In Table A.4, most common gases (air, nitrogen,...Ch. 1 - Prob. 1.36PCh. 1 - A near-ideal gas has a molecular weight of 44 and...Ch. 1 - In Fig. 1.7, if the fluid is glycerin at 20°C and...Ch. 1 - Prob. 1.39PCh. 1 - Glycerin at 20°C fills the space between a hollow...Ch. 1 - An aluminum cylinder weighing 30 N, 6 cm in...Ch. 1 - Prob. 1.42PCh. 1 - Prob. 1.43PCh. 1 - One type of viscometer is simply a long capillary...Ch. 1 - A block of weight W slides down an inclined plane...Ch. 1 - A simple and popular model for two nonnewtonian...Ch. 1 - Data for the apparent viscosity of average human...Ch. 1 - A thin plate is separated from two fixed plates by...Ch. 1 - An amazing number of commercial and laboratory...Ch. 1 - Prob. 1.50PCh. 1 - Prob. 1.51PCh. 1 - The belt in Fig. P1.52 moves at a steady velocity...Ch. 1 - A solid tune of angle 2 , base r0, and density...Ch. 1 - A disk of radius R rotates at an angular velocity ...Ch. 1 - A block of weight W is being pulled over a table...Ch. 1 - The device in Fig. P1.56 is called a cone-plate...Ch. 1 - Extend the steady flow between a fixed lower plate...Ch. 1 - The laminar pipe flow example of Prob. 1.12 can be...Ch. 1 - A solid cylinder of diameter D, length L, and...Ch. 1 - Prob. 1.60PCh. 1 - Prob. 1.61PCh. 1 - P1.62 The hydrogen bubbles that produced the...Ch. 1 - Derive Eq. (1.33) by making a force balance on the...Ch. 1 - Pressure in a water container can be measured by...Ch. 1 - The system in Fig. P1.65 is used to calculate the...Ch. 1 - Prob. 1.66PCh. 1 - Prob. 1.67PCh. 1 - Prob. 1.68PCh. 1 - A solid cylindrical needle of diameter d, length...Ch. 1 - Derive an expression for the capillary height...Ch. 1 - A soap bubble of diameter D1coalesces with another...Ch. 1 - Early mountaineers boiled water to estimate their...Ch. 1 - A small submersible moves al velocity V, in fresh...Ch. 1 - Oil, with a vapor pressure of 20 kPa, is delivered...Ch. 1 - An airplane flies at 555 mi/h. At what altitude in...Ch. 1 - Prob. 1.76PCh. 1 - Prob. 1.77PCh. 1 - P1.78 Sir Isaac Newton measured the speed of sound...Ch. 1 - Prob. 1.79PCh. 1 - Prob. 1.80PCh. 1 - Use Eq. (1.39) to find and sketch the streamlines...Ch. 1 - P1.82 A velocity field is given by u = V cos, v =...Ch. 1 - Prob. 1.83PCh. 1 - In the early 1900s, the British chemist Sir Cyril...Ch. 1 - Prob. 1.85PCh. 1 - A right circular cylinder volume v is to be...Ch. 1 - The absolute viscosity of a fluid is primarily a...Ch. 1 - Prob. 1.2FEEPCh. 1 - Helium has a molecular weight of 4.003. What is...Ch. 1 - An oil has a kinematic viscosity of 1.25 E-4 m2/s...Ch. 1 - Prob. 1.5FEEPCh. 1 - Prob. 1.6FEEPCh. 1 - FE1.7 Two parallel plates, one moving at 4 m/s...Ch. 1 - Prob. 1.8FEEPCh. 1 - A certain water flow at 20°C has a critical...Ch. 1 - Prob. 1.10FEEPCh. 1 - Sometimes we can develop equations and solve...Ch. 1 - When a person ice skates, the surface of the ice...Ch. 1 - Two thin flat plates, tilted at an angle a, are...Ch. 1 - Oil of viscosity and density drains steadily...Ch. 1 - Prob. 1.5CPCh. 1 - Prob. 1.6CPCh. 1 - Prob. 1.7CPCh. 1 -
C1.8 A mechanical device that uses the rotating...Ch. 1 - Prob. 1.9CPCh. 1 - A popular gravity-driven instrument is the...Ch. 1 - Mott [Ref. 49, p. 38] discusses a simple...Ch. 1 - A solid aluminum disk (SG = 2.7) is 2 in in...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Cold water enters a pipe, where it is heated by an external heat source . The inlet and outlet water temperatures are Tin and Tout, respectively. The total rate of heat transfer Q. from the surroundings into the water in the pipe is Q. = m·cp(Tout − Tin) where m . is the mass flow rate of water through the pipe, and cp is the specific heat of the water. Write the primary dimensions of each additive term in the equation, and verify that the equation is dimensionally homogeneous. Show all your work.arrow_forwardUsing the following dimensional scales x' = x/l; y' = y/l; u' = u/U; v' = v/U; p' = p/(pU²); B' = B/(pU²/1); 0 = (T-T.)/AT; Re = UL/v; Pr = v/a; Sc = v/Dab, show that the governing equations can be written in the following non-dimensional form: continuity: x-motion: y-motion: Energy: Species a: du' ax' u +3y= 0 u' du' ax' Əx' +v' du' Əy' +v'. == ay' 30 u' +v'. Əx' ƏWA ax' де dy! +v' aw A Əy' др' ax' (0²u' a²u' + + 2/12 (3²1/²/² + 0²1/²1) + Bx Reax¹² dy' = ap' -1 (2²0² + 3²1/²) + By + ay' Reax¹² dyr² 1 a²0 a²0 dyr² Re Prax¹² + 1 ResTWA +2 J²WA ax¹2 ay ¹2arrow_forwardIf the following equation is dimensionally homogeneous, find the dimensions of the physical quantity K indicated in the system of fundamental physical quantities: Length, Mass and Time. Ep -G Mm K where Ep is the gravitational potential energy (same units as the kinetic energy E mv²/2), M and m are the mass of the earth and the mass of the body, respectively, and G is the universal gravitation constant G~ 6,67 x 10-11 N m² kg²arrow_forward
- 1:54 3.11 A satellite in earth orbit has perigee and apogee radii ofr, = 7500km and r, = 16,000 km, respectively. Find its true anomaly 40 min after passing the true anomaly of 80°. (Ans.: 174.7°)arrow_forwardAn engineer would like to create a formula to determine the force exerted by a river flow on a bridge column. The figure of the problem is shown here in front and top views. Front view 18 |h Water properties V, P, μ Top view of This problems is similar but not the same of the exercise I solved in the class notes. Note that there are more variables which may be relevant for this problem, such as the gravity g and the flow depth h. Use the Buckingham Pi Theory to find an expression for the force F. 1) What popular non-dimensional numbers do you see? 2) What is the expression of the force?arrow_forwardA bullet is to be tested in the laboratory to determine the drag force on it. Dependent parameter the drag force D (Newton) depends on the velocity of the bullet V(m/s), the length of the bullet L(m), sound velocity c(m/s), density of fluid ρ (kg/m3) and dynamic viscosity µ(kg/ms). Solve the problem by making the necessary assumptions and drawing the schematic figure. I-Determine the nondimensional p parameters using repeating variables ii-a bullet with a speed of 96,2 m/s in air may be modelled in a water tunnel with a test section velocity of 262 cm/s. Determine the length of the model, if the length of the bullet is 56,2 mm. The air and water temperature is 20 oC degree at 1 atm. iii- if the drag force on the model is measured to be 2,62 N, then determine the expected drag force on the bullet. Comment on dynamic similarity equivalence?arrow_forward
- The modulus k of a coil spring (force required to stretch the spring a unit distance) can be expressed in equation form as k=(Gr^4)/(4R^3n) in which r and R are lengths and n is a dimensionless number. Determine the dimensions of G (a property of the spring material) .arrow_forwardThe air resistance to the motion of a vehicle is something important that engineers investigate. As you may also know, the drag force acting on a car is determined experimentally by placing the car in a wind tunnel. For a given car, the experimental data is generally represented by a single coefficient that is called the drag coefficient. It is given by the relationship: Cd = Fd/(1/2)pV2A. What is the appropriate unit for Cd if the preceding equation is to be homogeneous in units?arrow_forwardMechanical Engineering The following equation is used to calculate a change in the kinetic energy of a moving mass: KE = 0.5 * m * (v2 - u2) Where the quantities are: the kinetic energy KE (in Joules), the mass m (in kg), the initial velocity u (in m/s) and the final velocity v (in m/s). Determine if the equation is dimensionally homogeneous or not.arrow_forward
- 3- Use dimensional analysis to show that in a problem involving shallow water waves, both the Froude number and the Reynolds number are relevant dimensionless parameters. The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g. fluid density p, and fluid viscosity μ. Manipulate your's to get the parameters into the following form: Fr= √=f(Re) where Re=pch μ h Too 8 P₂ μarrow_forwardConsider the following equation. All three of the terms in parentheses are dimensionless groups. Because kC is difficult to determine directly, the other variables are measured and kC is calculated from the given equation. What is the estimated value of kC? What are the units of kC? Show your work. The following values were measured: D = 8.0 mm, DAB = 0.475 cm2/s, μ = 1.12 x 10–3 N-s/m2, ρ = 1.00 x 10–3 g/cm3, v = 15.0 m/s. Note: Given Equation attached belowarrow_forwardHow much heat is absorbed by a 27.0 g sample of water in going from liquid at 38.2 °C to steam at 119 °C and a pressure of 1.00 atm? Use the data in the following table. Express your answer in kilojoules. Pay attention to units! Some Thermal Properties of Water Property Specific heat (J/g °C) Solid Liquid Gas AHfusion (kJ/mol; at 0 °C) A Hvaporization (kJ/mol; at 100 °C) A Hsublimation (kJ/mol) Melting point (°C) Boiling point (°C) Answer: Value 2.07 4.18 2.01 6.01 40.6 50.9 0 100arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Unit Conversion the Easy Way (Dimensional Analysis); Author: ketzbook;https://www.youtube.com/watch?v=HRe1mire4Gc;License: Standard YouTube License, CC-BY