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,
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Fluid Mechanics: Fundamentals and Applications
- In the study of turbulent flow, turbulent viscous dissipation rate ? (rate of energy loss per unit mass) is known to be a function of length scale l and velocity scale u′ of the large-scale turbulent eddies. Using dimensional analysis (Buckingham pi and the method of repeating variables) and showing all of your work, generate an expression for ? as a function of l and u′.arrow_forward7-67 A liquid of density p and viscosity u is pumped at volume flow rate b through a pump of diameter D. The blades of the pump rotate at angular velocity w. The pump supplies a pressure rise AP to the liquid. Using dimensional analysis, generate a dimensionless relationship for AP as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. Hint: For consistency (and whenever possible), it is wise to choose a length, a density, and a velocity (or angular velocity) as repeating variables.arrow_forwardGiven a mechanical system shown in the figure. What is the differential equation at mass (M2)? (ILO2) K₁ moo f(t) M₂ + B12 d2x dt² Option 1 M, Option 3 d(x₂-x1) dt B. + K₂X₂ = 0 M₂²x + K₂X₂ = 0 dt² M₂ mon K₂ d²x2 + B12 M₂ dt² Option 2 M₂ dt² + B12 Option 4 dx2 dt dx₂ dt + K₂x₂ = 0 ²+ K2₂ (x₂-x₁) = 0arrow_forward
- Ship whose full length is 100 m is to travel at 10 m/sec. For dynamical similarity, with what velocity should a 1:25 model of the ship be towed?arrow_forwardin results. 1-26. Equal layers of two immiscible fluids are being sheared between a moving and a fixed plate, as in Fig. P1-26. Assuming linear velocity profiles, find an expression for the interface velocity U as a function of V, ₁. and 4₂. h/2 h/2 y U? H₂ 4₂ Fixed FIGURE P1-26arrow_forwardIn making a dimensional analysis, what rules do you followfor choosing your scaling variables?arrow_forward
- First Order Differential Equations are inherent in almost all aspects of engineering, e.g., electronics (RC/RL circuits or charge/discharge of capacitors), thermodynamics (i.e., Newton’s Law of Cooling), mechanical systems (stress/strain) etc. In fact, virtually anywhere there are time varying dynamics. You need to demonstrate how different engineering systems models are used to solve them using first-order differential equations.arrow_forwardA stirrer is used to mix chemicals in a large tank. The shaft power W . supplied to the stirrer blades is a function of stirrer diameter D, liquid density ? ,liquidviscosity ? , and the angular velocity ? of the spinning blades.Use the method of repeating variables to generate a dimensionless relationship between these parameters. Show all your work and be sure to identify your Π groups, modifying them as necessary.arrow_forwardThe viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: T and a, PND? b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750kg/m² and the dynamic viscosity is 0.2 N.s/m². For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s/m². kg.m IN =1arrow_forward
- Physical Properties: https://education.wiley.com/player/index.html#/res;url=https:%2F%2Feducation.wiley.com%2Fcontent%2FBergman_Fund_Heat_Mass_8e%2Febook%2Fepub%2F9781119353881%2FOPS%2Fa01.xhtml%23headda01 Mathematical Functions: https://education.wiley.com/player/index.html#/res;url=https:%2F%2Feducation.wiley.com%2Fcontent%2FBergman_Fund_Heat_Mass_8e%2Febook%2Fepub%2F9781119353881%2FOPS%2Fa02.xhtml%23headda01arrow_forwardA stirrer is used to mix chemicals in a tank let tank diameter Dtank and average liquid depth htank. The shaft power W . supplied to the stirrer blades is a function of stirrer diameter D, liquid density ? ,liquidviscosity ? , and the angular velocity ? of the spinning blades.Use the method of repeating variables to generate a dimensionless relationship between these parameters. Show all your work and be sure to identify your Π groups, modifying them as necessary.arrow_forwardAn engineer is to design a human powered submarine for a design competition. The overall length of the prototype submarine is 2.24 m and its engineer designers hope that it can travel fully submerged through water at 0.560 m/s. The water is freshwater (a lake) at 7-15°C (p=999.1 kg/m3 and u= 1.138 ×103 kg/m-st. The design team builds a one-eighth scale model to test in their university's wind tunnel. The air in the wind tunnel is at 25°C (p= 1.180 kg/m3 and u = 1.849 ×10-5 kg/m-s) and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achieve similarity?arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning