The Reynolds number for a 1-ft-diameter sphere moving at2.3 mi/h through seawater (specifi c gravity 1.027, viscosity1.07 E-3 N ? s/m 2 ) is approximately( a ) 300, ( b ) 3000, ( c ) 30,000, ( d ) 300,000, ( e ) 3,000,000
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The Reynolds number for a 1-ft-diameter sphere moving at
2.3 mi/h through seawater (specifi c gravity 1.027, viscosity
1.07 E-3 N ? s/m 2 ) is approximately
( a ) 300, ( b ) 3000, ( c ) 30,000, ( d ) 300,000, ( e ) 3,000,000
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- The 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 / σWe are given laboratory data, taken by Prof. Robert Kirchhoffand his students at the University of Massachusetts, for thespin rate of a 2-cup anemometer. The anemometer wasmade of ping-pong balls ( d = 1.5 in) split in half, facing inopposite directions, and glued to thin ( 1/4-in) rods pegged toa center axle. There were fourrods, of lengths l = 0.212, 0.322, 0.458, and 0.574 ft. Theexperimental data, for wind tunnel velocity U and rotationrate Ω , are as follows: Assume that the angular velocity Ω of the device is afunction of wind speed U , air density ρ and viscosity μ , rodlength l , and cup diameter d . For all data, assume air is at1 atm and 20 ° C. Defi ne appropriate pi groups for thisthe problem, and plot the data in this dimensionless manner.Comment on the possible uncertainty of the results.As a design application, suppose we are to use thisanemometer geometry for a large-scale ( d = 30 cm) airportwind anemometer. If wind speeds vary up to 25 m/s and wedesire an average…A sample of powdered zinc oxide, density 5.60g/cm 3 , is allowed to settle under the accelerationof gravity, 981 cm/sec 2 , at 25 25°C. The rate ofsettling, v, is 7.30 ×10 3 cm/sec; the density ofthe medium is 1.01 g/cm 3 , and its viscosity is 1centipoise = 0.01 poise or 0.01 g/cm sec.Calculate the Stokes diameter of the zinc oxidepowder.Problem:
- Determine the Prandtl number, Nusselt number, and Reynolds number from the following flow data: cp = 0.5 Btu/lbmR k = 2 Btu/h-ft-R h = 20 Btu/h-ft2-R dynamic viscosity = 0.222 lbm/ft-s v = 5ft/s D = 2in Density=58 lbm/ft3A dimensionless combination of variables that is important in the study of viscous flow through pipes is called the Reynolds number, Re, defined as ???/? where, as indicated in Fig. 11, ? is the fluid density, V the mean fluid velocity, D the pipe diameter, and the fluid viscosity. A Newtonian fluid having a viscosity of 0.38 ? . ?/?² and a specific gravity of 0.91 flows through a 25‐mmdiameter pipe with a velocity of 2.6 ?/?. Determine the value of the Reynolds number using (a) SI units, and (b) BG units.Books on porous media and atomization claim that the viscosityμ and surface tension Y of a fl uid can be combinedwith a characteristic velocity U to form an important dimensionlessparameter. ( a ) Verify that this is so. ( b ) Evaluatethis parameter for water at 20°C and a velocity of3.5 cm/s. Note: You get extra credit if you know the nameof this parameter.
- A curved blood vessel has an internal diameter ? = 5 mm and a radius of curvature of ?? = 17 mm. Blood has a density of ρ = 1060 kg/m3 and a viscosity of 3.5 cP, and travels at an average velocity of ? = 1 m/s. a) Comment on the nature of the flow with reference to relevant non-dimensional groups. b) Can the flow be modelled using the Hagen-Poisseuile equation? If not, explain what specific assumptions are invalid. c) The viscosity of blood is measured and is shown in Figure Q2. Consider two long straight blood vessels with steady flow. The diameter of the first vessel is 5 mm and the average velocity is 6 cm/s. The internal diameter of the second vessel is 2.2 mm and the average velocity is 50 cm/s. Which vessel would you expect the Hagen-Poisseiulle equation to be more accurate in? Explain your answer (1-2 sentences).Under laminar conditions, the volume flow Q through asmall triangular-section pore of side length b and length Lis a function of viscosity μ , pressure drop per unit length∆p / L , and b . Using the pi theorem, rewrite this relation indimensionless form. How does the volume flow change ifthe pore size b is doubled?The Ekman number, Ek, arises in geophysical fluiddynamics. It is a dimensionless parameter combining seawaterdensity ρ , a characteristic length L , seawaterviscosity μ , and the Coriolis frequency Ω sin φ , where Ωis the rotation rate of the earth and φ is the latitude angle.Determine the correct form of Ek if the viscosity is in thenumerator.
- When fluid in a pipe is accelerated linearly from rest, itbegins as laminar flow and then undergoes transition toturbulence at a time t tr that depends on the pipe diameterD , fluid acceleration a , density ρ , and viscosity μ .Arrange this into a dimensionless relation between t trand D .A thin flat plate 55 x 110 cm is immersed in a 6 m/s stream of oil. What is the friction drag on one side of the plate if the flow is parallel to the long side? Use the density of oil as 891 kg/m3 and absolute viscosity of 0.29 Pa-s. a. 90 N b. 102 N c. 145 N d. 181 NConsider laminar flow through a long section of pipe, as in Fig. For laminar flow it turns out that wall roughness is not a relevant parameter unless ? is very large. The volume flow rate V· through the pipe is a function of pipe diameter D, fluid viscosity ? , and axial pressure gradient dP/dx. If pipe diameter is doubled, all else being equal, by what factor will volume flow rate increase? Use dimensional analysis.