Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 1, Problem 1.29P
To determine
The value of energy in
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Recall that the CWH equation involves two important assumptions. Let us investigate how these
assumptions affect the accuracy of state trajectories under the control inputs optimized in (a) and (b).
(c.1): Discuss the assumptions about the chief and deputy orbits that are necessary for deriving CWH.
PROBLEM 2.50
1.8 m
The concrete post (E-25 GPa and a
=
9.9 x 10°/°C) is reinforced with six
steel bars, each of 22-mm diameter (E, = 200 GPa and a, = 11.7 x 10°/°C).
Determine the normal stresses induced in the steel and in the concrete by a
temperature rise of 35°C.
6c
"
0.391 MPa
240 mm
240 mm
6₁ =
-9.47 MPa
For some viscoelastic polymers that are subjected to stress relaxation tests, the stress decays with
time according to
a(t) = a(0) exp(-4)
(15.10)
where σ(t) and o(0) represent the time-dependent and initial (i.e., time = 0) stresses, respectively, and t and T denote
elapsed time and the relaxation time, respectively; T is a time-independent constant characteristic of the material. A
specimen of a viscoelastic polymer whose stress relaxation obeys Equation 15.10 was suddenly pulled in tension to
a measured strain of 0.5; the stress necessary to maintain this constant strain was measured as a function of time.
Determine E (10) for this material if the initial stress level was 3.5 MPa (500 psi), which dropped to 0.5 MPa (70
psi) after 30 s.
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...
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- For the flows in Examples 11.1 and 11.2, calculate the magnitudes of the Δ V2 / 2 terms omitted in B.E., and compare these with the magnitude of the ℱ terms.arrow_forwardCalculate ℛP.M. in Example 11.2.arrow_forwardQuestion 22: The superheated steam powers a steam turbine for the production of electrical power. The steam expands in the turbine and at an intermediate expansion pressure (0.1 MPa) a fraction is extracted for a regeneration process in a surface regenerator. The turbine has an efficiency of 90%. It is requested: Define the Power Plant Schematic Analyze the steam power system considering the steam generator system in the attached figure Determine the electrical power generated and the thermal efficiency of the plant Perform an analysis on the power generated and thermal efficiency considering a variation in the steam fractions removed for regeneration ##Data: The steam generator uses biomass from coconut shells to produce 4.5 tons/h of superheated steam; The feedwater returns to the condenser at a temperature of 45°C (point A); Monitoring of the operating conditions in the steam generator indicates that the products of combustion leave the system (point B) at a temperature of 500°C;…arrow_forward
- This is an old practice exam question.arrow_forwardSteam enters the high-pressure turbine of a steam power plant that operates on the ideal reheat Rankine cycle at 700 psia and 900°F and leaves as saturated vapor. Steam is then reheated to 800°F before it expands to a pressure of 1 psia. Heat is transferred to the steam in the boiler at a rate of 6 × 104 Btu/s. Steam is cooled in the condenser by the cooling water from a nearby river, which enters the condenser at 45°F. Use steam tables. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the pressure at which reheating takes place. Use steam tables. Find: The reheat pressure is psia. (P4)Find thermal efficiencyFind m dotarrow_forwardAir at T1 = 24°C, p1 = 1 bar, 50% relative humidity enters an insulated chamber operating at steady state with a mass flow rate of 3 kg/min and mixes with a saturated moist air stream entering at T2 = 7°C, p2 = 1 bar. A single mixed stream exits at T3 = 17°C, p3 = 1 bar. Neglect kinetic and potential energy effects Determine mass flow rate of the moist air entering at state 2, in kg/min Determine the relative humidity of the exiting stream. Determine the rate of entropy production, in kJ/min.Karrow_forward
- Air at T1 = 24°C, p1 = 1 bar, 50% relative humidity enters an insulated chamber operating at steady state with a mass flow rate of 3 kg/min and mixes with a saturated moist air stream entering at T2 = 7°C, p2 = 1 bar. A single mixed stream exits at T3 = 17°C, p3 = 1 bar. Neglect kinetic and potential energy effects Determine mass flow rate of the moist air entering at state 2, in kg/min Determine the relative humidity of the exiting stream. Determine the rate of entropy production, in kJ/min.Karrow_forwardAir at T1 = 24°C, p1 = 1 bar, 50% relative humidity enters an insulated chamber operating at steady state with a mass flow rate of 3 kg/min and mixes with a saturated moist air stream entering at T2 = 7°C, p2 = 1 bar. A single mixed stream exits at T3 = 17°C, p3 = 1 bar. Neglect kinetic and potential energy effects (a) Determine mass flow rate of the moist air entering at state 2, in kg/min (b) Determine the relative humidity of the exiting stream. (c) Determine the rate of entropy production, in kJ/min.Karrow_forwardA simple ideal Brayton cycle operates with air with minimum and maximum temperatures of 27°C and 727°C. It is designed so that the maximum cycle pressure is 2000 kPa and the minimum cycle pressure is 100 kPa. The isentropic efficiencies of the turbine and compressor are 91% and 80%, respectively, and there is a 50 kPa pressure drop across the combustion chamber. Determine the net work produced per unit mass of air each time this cycle is executed and the cycle’s thermal efficiency. Use constant specific heats at room temperature. The properties of air at room temperature are cp = 1.005 kJ/kg·K and k = 1.4. The fluid flow through the cycle is in a clockwise direction from point 1 to 4. Heat Q sub in is given to a component between points 2 and 3 of the cycle. Heat Q sub out is given out by a component between points 1 and 4. An arrow from the turbine labeled as W sub net points to the right. The net work produced per unit mass of air is kJ/kg. The thermal efficiency is %.arrow_forward
- Steam enters the high-pressure turbine of a steam power plant that operates on the ideal reheat Rankine cycle at 700 psia and 900°F and leaves as saturated vapor. Steam is then reheated to 800°F before it expands to a pressure of 1 psia. Heat is transferred to the steam in the boiler at a rate of 6 × 104 Btu/s. Steam is cooled in the condenser by the cooling water from a nearby river, which enters the condenser at 45°F. Use steam tables. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the pressure at which reheating takes place. Use steam tables. The reheat pressure is psia.Find thermal efficieny Find m dotarrow_forwardThis is an old exam practice question.arrow_forwardAs shown in the figure below, moist air at T₁ = 36°C, 1 bar, and 35% relative humidity enters a heat exchanger operating at steady state with a volumetric flow rate of 10 m³/min and is cooled at constant pressure to 22°C. Ignoring kinetic and potential energy effects, determine: (a) the dew point temperature at the inlet, in °C. (b) the mass flow rate of moist air at the exit, in kg/min. (c) the relative humidity at the exit. (d) the rate of heat transfer from the moist air stream, in kW. (AV)1, T1 P₁ = 1 bar 11 = 35% 120 T₂=22°C P2 = 1 bararrow_forward
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