Consider ventilation of a well-mixed room as in Fig. P7-21. The differential equation for mass concentration in the room as a function of time is given in Prob. 7-21 and is repeated here for convenience,
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Fluid Mechanics: Fundamentals and Applications
- When fluid in a pipe is accelerated linearly from rest, it begins as laminar flow andthen undergoes transition to turbulence at a time ttr which depends upon the pipe diameter D,fluid acceleration a, density ρ, and viscosity µ. Arrange this into a dimensionless relationbetween ttr and D.arrow_forwardchoose whether the statement is true or false and discuss your answer brieflyGeometric similarity is a necessary condition for kinematic similari ty.arrow_forwardWrite the primary dimensions of the universal ideal gas constant Ru. (Hint: Use the ideal gas law, PV = nRuT where P is pressure, V is volume, T is absolute temperature, and n is the number of moles of the gas.)arrow_forward
- When fluid in a pipe is accelerated linearly from rest, it begins as laminar flow andthen undergoes transition to turbulence at a time ttr which depends upon the pipe diameter D,fluid acceleration a, density ρ, and viscosity µ. Arrange this into a dimensionless relationbetween ttr and D. (Fluid Mechanics)arrow_forwardIn making a dimensional analysis, what rules do you followfor choosing your scaling variables?arrow_forwardHow do you datum dimension the isometric view?arrow_forward
- The drag coefficient in aircraft industry affected by some parameters which are thespeed of plane (v), the plane length (L), the air density (ρ), the air dynamic viscosity(μ), and speed of sound (a). By using dimensional analysis, identify two non-dimensionnumbers in which the drag coefficient is a function of them and explain how these twowill effect on drag coefficient.arrow_forwardHow do you derive the Kinematic Differential Equation of the Euler Parameters? I just want to know how we get the final matrix. For e4dot, e4 = (1/2)sqrt(1 + C11 + C22 + C33), e4dot = (1/4)*(1 + C11 + C22 + C33)^(-1/2) * (C11dot + C22dot + C33dot). From the C11dot, C22dot, and C33 dot equations we get e4dot = -(1/2)*(w1e1 + w2e2 + w3e3). I get how to get e4. How do I get the other 3 Euler Parameters? Please give detailed steps. The final equations should look like the image.arrow_forwardConsider fully developed flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary. The flow is steady, incompressible, and two-dimensional in the xy-plane. a) Use the first principle (dimensional analysis) to generate a dimensionless relationship for the x-component of fluid velocity u as a function of fluid viscosity μ, top plate speed v, distance h, fluid density ρ, and distance y. b) Name the common dimensionless number formed in (a). Hint: modifying the dimensionless number if necessary.arrow_forward
- The Stokes-Oseen formula for drag force on a sphere at low speed is given asD = 3dV +916V 2d2, where D is drag, V is velocity, is density, d is the sphere diameter, and is the viscosity coe¢ cient.(a) Using the formula given, Önd the dimensions of the viscosity coe¢ cient. (Donít simply look upthe dimensions; use the formula to show them.) Be sure to show your work. Find the primaryunits of viscosity in SI and British units.(b) Verify that the Stokes-Oseen formula is dimensionally homogeneous.arrow_forwardDirections: Solve the following problems completely, and make a detailed solution. Any incompletesolution arriving at such answers will never be considered. 5. A certain gas weighs 3.19 x 10-3 slugs/ft3 at a certain temperature and pressure. Whatare the values of its density (N/m3), specific volume (m3/kg), and specific gravity relativeto air weighing 2.39 x 10-3 slugs/ft3?arrow_forwardThe answer will be 9.554x10^-4 but I can’t figure out how to get there. Please use dimensional analysisarrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning