Sometimes we can develop equations and solve practical problems by knowing nothing more than the dimensions of the key parameters in the problem. For example, consider the heal Joss through a window in a building. Window efficiency is rated in terms of "R value," which has units of (ft2 · h · °F)/Btu. A certain manufacturer advertises a double-pane window with an R value of 2,5. The same company produces a. triple-pane window with an R value of 3.4. In either case the window dimensions are 3 ft by 5 ft. On a given winter day, the temperature difference between the inside and outside of the building is 45°F. (a) Develop an equation for the amount of heat lost in a given time period
(b) How much heat (in Btu) is lost through the triple-pane window in one 24-h period?
(c) Suppose the building is heated with propane gas, which costs $3.25 per gallon. The propane burner is HO percent efficient. Propane has approximately 90,000 Btu of available energy per gallon. In that same 24-h period, how much money would a homeowner save per window by installing triple-pane rather than double-pane windows?
(d) Finally, suppose the homeowner buys 20 such triple-pane windows for the house. A typical winter has the equivalent of about 120 heating days at a temperature difference of 45°F. Each triple-pane window costs $85 more than the double-pane window. Ignoring interest and inflation, how many years will it take the homeowner to make up the additional cost of the triple-pane windows from heating bill savings?
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
Fluid Mechanics
- When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the weight of the sphere is balanced by the buoyant force and the frictional resistance of the fluid. Make a dimensional analysis of this problem and indicate how experimental data for this problem could be correlated. Neglect compressibility effects and the influence of surface roughness.arrow_forward5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.arrow_forwardThe power P required to drive a propeller is known to depend on the diameter of the propeller D, the density of fluid ρ, the speed of sound a, the angular velocity of the propeller ω, the freestream velocity V , and the viscosity of the fluid µ. (a) How many dimensionless groups characterize this problem? (b) If the effects of viscosity are neglected, and if the speed of sound is not an important variable, express the relationship between power and the other variables in nondimensional form. (c) A one-half scale model of a propeller is built, and it uses Pm horsepower when running at a speed ωm. If the full-scale propeller in the same fluid runs at ωm/2, what is its power consumption in terms of Pm if the functional dependence found in part (b) holds? What freestream velocity should be used for the model test?arrow_forward
- Two endlessly long flat plates, separated by 3 inches in distance but with a thickness of 5 inches, each transport alcohol (5 m/s, 1 Pa·s, S.G. 0.89 (ref. water at 4 degrees Celsius) to a given location with a specific velocity. Prove that the Reynold's number of the following problem is a value approximately around 90-100.arrow_forwardConsider a boundary layer growing along a thin flat plate. This problem involves the following parameters: boundary layer thickness ? , downstream distance x, free-stream velocity V, fluid density ? , and fluid viscosity ? . The number of primary dimensions represented in this problem is (a) 1 (b) 2 (c) 3 (d ) 4 (e) 5arrow_forwardA new implantable drug delivery device is being developed in your lab. The device prototype is a very thin strip (0.1mm × 1mm × 15mm) of polymer coated on both sides with 22 milligrams of solid drug particles. To test the drug delivery profile, you "implant the device by suspending it in a homogenous model fluid that has following properties: viscosity = 0.0018 Pa.s, density = 1.32 g cm^-3, temperature = 37°C. The diffusivity of the drug is estimated to be 2.113×10^-6 cm^2/S. 1. Determine how far the drug would penetrate into the fluid in 2.2 hours.arrow_forward
- Which choice is not a scaling parameter used to nondimensionalize the equations of motion? (a) Characteristic length, L (b) Characteristic speed, V (c) Characteristic viscosity, ? (d ) Characteristic frequency, f (e) Gravitational acceleration, garrow_forwardWrite the primary dimensions of each of the following variables from the field of thermodynamics, showing all your work: (a) energy E; (b) specific energy e = E/m; (c) power W . .arrow_forwardAlthough we usually think of a model as being smaller than the prototype, describe at least three situations in which it is better for the model to be larger than the prototype.arrow_forward
- A square block weighing 1.1 KN and 250 mm on an edge slides down an 20 degrees inclined on a film of oil 6.0 micrometer thick. Assuming a linear velocity profile in the oil, what is the terminal speed of the block in m/s. The viscosity of the oil is 7 mPa-s. a.5.16 b.5.62 c.5.75 d.5.48arrow_forwardA sphere is moving in water with a velocity of 1.6 m/s. Another sphere of twice the diameter is placed in a wind tunnel and tested with air which is 750 times less dense and 60 times less viscous (dynamically) than water. The velocity of air that will model dynamically similar conditions isarrow_forwardThe 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_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning