An important application of fluid
where
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Fluid Mechanics: Fundamentals and Applications
- During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumedthat the energy released E , was a function of blast waveradius R , air density ρ, and time t . Arrange these variablesinto a single dimensionless group, which we may term theblast wave number .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_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
- In making a dimensional analysis, what rules do you followfor choosing your scaling variables?arrow_forwardThe volume flow Q through an orifice plate is a function ofpipe diameter D , pressure drop D p across the orifice, fluiddensity ρ and viscosity μ , and orifice diameter d . Using D ,ρ , and ∆ p as r e peating variables, express this relationshipin dimensionless form.arrow_forwardDefine the following dimensionless group number in fluid mechanics, a)Interpretation of force ratio, and what types of application. b)Reynolds number (Re) c)Euler number (Eu) d) Mach number (Ma) e) Weber number (We)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_forwardA block of weight W slides down an inclined plane whilelubricated by a thin fi lm of oil, as in Fig. P1.45. The fi lmcontact area is A and its thickness is h . Assuming a linearvelocity distribution in the fi lm, derive an expression forthe “terminal” (zero-acceleration) velocity V of the block.Find the terminal velocity of the block if the block mass is6 kg, A = 35 cm 2 , θ = 15 ° , and the fi lm is 1-mm-thick SAE30 oil at 20 ° C.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_forward
- In CFD lingo, the stream function is often called a non-primitive variable, while velocity and pressure are called primitive variables. Why do you suppose this is the case?arrow_forwardThe only possible dimensionless group that combines velocityV , body size L , fl uid density ρ , and surface tensioncoeffi cient σ is( a ) L ρσ / V , ( b ) ρ VL 2 / σ , ( c ) ρσ V 2 / L , ( d ) σ LV 2 / ρ ,( e ) ρ LV 2 / σarrow_forwardThe Ekman number, important in physical oceanography,is a dimensionless combination of μ , L , ρ , and the earth’srotation rate Ω . If the Ekman number is proportional to Ω ,it should take the form( a ) ρΩ2L2/μ, ( b ) μΩL/ρ, ( c ) ρΩL/μ, ( d ) ρΩL2/μ,( e ) ρΩ/Lμarrow_forward
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