1.5. The terminal velocity t, attained by a aphorical particle of radius r, and

Question

1.5. The terminal velocity t, attained by a aphorical particle of radius r, and density o, while falling through a viscous medium is given by Stoken' law where p. and un are the density and absolute viscosity of the medium, respectively, and g is the local acceleration of gravity (a) Show that the above equation is dimensionally homogeneous. (b) Modify the equation to accept direetly the following (inconsistent) units: u.-ft./min, g-32. 17 ft/sec, r," mm, "-cp, and specific gravities (water :: 1) instead of densities. Ana, (2g/9) becomes 428.6. (c) The dispersed water droplets in a crude oil emulsion have an averag radius of 5 microns (1 micron -0.001 mm) and a specific gravity of 1.08. The continuous cil phase has a specific gravity of 0.858 and a viscosity of 90 cp. How many hours would be required for these water droplets to settle 6 ft? Ans. 378 hr.

Explanation / Answer

a) we know that L.H.S. = dimensions of velocity = meter/sec = m/s

now R.H.S. dimensions = (dimensions of g * dimensions of density * (dimensions of radius)2)/dimensions of absolute viscocity

= ((m/s2)*(kg/m3)*m2)/(kg/m.s) = m/s if solved

this means L.H.S = R.H.S or the equation is dimensionwise homogeneous.

ii) g = m/s2 = 32.17 ft/sec2

V = 2* 32.17/9 ft/s2 *(spgrp-spgrm)* (rp)2 /(cP) = 7.14*(spgrp-spgrm)* (rp)2 /(cP) ft/sec

7.14*60*(spgrp-spgrm)* (rp)2 /(cP) ft/min= 428.9*(spgrp-spgrm)* (rp)2 /(cP) ft/min

iii) putting the numbers in equation obtained in (ii) part:

V (ft/minute ) = 428.9*(1.08-0.858)*(0.0052)/9 = 2.64x10-4 ft/min

time = distance/velocity = 6/(2.64x10-4) = 22685.3 minutes = 378 hrs

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.