Concept explainers
Fluid fills the space between two parallel plates. The differential equation that describes the instantaneous fluid velocity for unsteady flow with the fluid moving parallel to the walls is
The lower plate is stationary and the upper plate oscillates in the x-direction with a frequency ω and an amplitude in the plate velocity of U. Use the characteristic dimensions to normalize the differential equation and obtain the dimensionless groups that characterize the flow.
P7.4
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Additional Engineering Textbook Solutions
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
Thinking Like an Engineer: An Active Learning Approach (3rd Edition)
Fundamentals of Heat and Mass Transfer
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
DeGarmo's Materials and Processes in Manufacturing
Mechanics of Materials (10th Edition)
- A 5-kg object is acted upon by a horizontal force P=18t [N], where t is time in seconds. The coefficient of kinetic friction is µk = 0.15. At t = 2 s, the object's velocity is 10 m/s. Determine the velocity at t = 4 s. Use the Impulse-Momentum method. Provide the free-body diagram and show all work. Parrow_forwardMeasurements at a certain point of a pipe have been done where the following parameters were recorded: Fluid of density = 887 kg/m3, Fluid velocity = 4 m/s, Pressure= 11.3 KN/m2 If the total energy per unit weight at this point = 32 m, then the potential energy is:arrow_forwardThe wind flutter on the wing of a newly proposed jet fighter is given by the following 1st order differential equation: With the Boundary Condition: y(0) = 1 (remember this means that y = 1 when x = 0) Determine the vertical motion (y) in terms of the span (x) of the wing. The frequency of fluctuations of the wing at mach 2 is given by the non-homogenous 2nd order differential equation: With the boundary conditions: y(0) = 1 and y(1) = 0 (i.e., y = 1 when x = 0 and y = 0 when x = 1) By solving the homogenous form of this equation, complete the analysis and determine the amplitude (y) of vibration of the wing tip at mach 2. Critically evaluate wing flutter and fluctuation frequency amplitude determined by solving the two differential equations above.arrow_forward
- A small wind turbine is tested in a wind tunnel using the following model parameters: ρ = 1.2 kg/m3 , µ = 1.81x10-5 Ns/m2 , v = 12 m/s, A = 0.03 m2 and Cp is measured as 0.42. Assuming dynamic similarity exists, calculate the power output of a full-size turbine of diameter 60 m operating in air of density 1.3 kg/m3 and viscosity µ = 1.73x10-5 Ns/m2 with wind speeds of 15 m/sarrow_forwardWhile using the Heisler charts for a cylinder at time t = 10 sec and at a radial location of r/ro=0.6 =0.8 and Q/Qo= 0.7 where 0=T-T 0.=T.-T and 0 =T -T o o and Qo = PCPV(T¡-T∞) =0.4; 00 00 If the parameters associated with the cylinder are p=2700 kg/m and C =900 J/kg.C and volume of 1 m long cylinder = 0.1 m3 Calculate the maximum possible heat transfer from the cylinder to the environment per unit length of the cylinder if = 20°C; and T = 55 C T 00 Write only the numerical value after converting the unit in J/m.arrow_forwardA ship 350 m long moves in sea water whose density is 1030 kg/m3 . A 1:120 model of this ship is to be tested in a wind tunnel. The velocity of the wind tunnel around the model is 35 m/s and the resistance of the model is 65 N. Determine the velocity and also the resistance of the ship in sea water. The density of air is given as 1.24 kg/m3 . Take the kinematic viscosity of air and sea water as 0.012 stokes and 0.018 stokes respectively.arrow_forward
- A cylinder with diameter D, floats in a liquid as shown in the figure. When the cylinder is slightly offset with respect to its vertical axis, the cylinder will oscillate with a frequency w. Assume that this frequency is a function of the diameter, the mass of the cylinder, and the specific weight of the liquid. Determine, with the help of a dimensional analysis, how the frequency is related to these variables. If the mass of the cylinder increases, determine what happens with the frequency.arrow_forwardMeasurements at a certain point of a 1 point pipe have been done where the following parameters were recorded: Fluid of density = 887 kg/m3, Fluid velocity = 4 m/s, Pressure= 11.3 KN/m2 If the total energy per unit weight at this point = 32 m, then the potential energy is: Zero m 10 m 20 m 30 marrow_forwardThe paragraph below contains more than one instance of false statements or incorrect logic. In a short answer (50 words or less) based on transport and mathematical concepts, describe at least two errors in this paragraph that leads to the faulty conclusion. Consider a gas confined within a large sealed holding tank. Assume that the gas is stagnant (in the continuum sense) so that v = Q everywhere inside the tank. The continuity equation Dp Dp -p(V.v) applies to this gas. Since v= Q the continuity equation reduces to = 0. Dt Dt Integrating this equation gives the result that the density of the gas must be constant at every position inside the tank. Constant density means the gas is incompressible. Since everyone knows gases are actually compressible, the original assumption that y = 0 must be incorrect. Thus, we conclude that it is not possible to have storage tanks full of stagnant gas – there must always be some non-zero velocity.arrow_forward
- Given: U=Uoer/lsin(r/l) Find the above equation's dimensionless formarrow_forwardHome Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flowarrow_forwardConsider the fluid shown in the U-shaped tube of circular section R = 3 cm. This fluid of mass M and volumetric density: Describe simple harmonic oscillations. The harmonic oscillations of the fluid are governed by the differential equation: Figure 4 represents the acceleration as a function of the MAS time of the fluid. NOW ASSUME THAT THERE IS FRICTION OF THE LIQUID WITH THE WALLS OF THE CONTAINER. IN THIS CASE, THE OSCILLATIONS ARE DAMPERED WITH THE PASSAGE OF THE TIMEPO UNTIL THE BALANCE IS REACHED. IF THE AMPLKITUDE OF THE OSCILLATIONS DECAYS BY A FACTOR e ^ (- 6π) IN A TIME OF 2S. WHAT WILL BE THE FREQUENCY OF THE DAMPERED OSCILLATIONS?arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY