A solid sphere of radius R is rotating slowly at a constant angular velocity ' ' in a large body of quiescent fluid as shown in figure 2 (Appendix-I). Develop expressions for the pressure and velocity distributions in the fluid using shell momentum balances (refer figure 3). Also find out the torque required to maintain the motion. Assume that the sphere rotates sufficiently slowly so that one can conveniently use the creeping flow assumption. Appendix-A Figure 1: Velocity distribution and z-momentum Balance for the flow of a falling film on the outside of a circular tube. Figure 2: A slowly rotating sphere in an infinite expanse of fluid Figure 3: Differential Volume Elemen
Find the new location of point G, initially at G = [3 0 -1] If, (i) it is rotated by 60deg. about z-axis and then translated by 3 units along y-axis, and (ii) it is first translated by 3 units along y-axis and then rotated by 60deg bout z-axis. Are the two locations same? Check and justify, whether the final position in two cases is same or different.
Given the following contingency table for hair colour and eye colour. Find
the value of Chi-square. Is there good association between the two?
Hair Colour
Fair Brown Black
Eye Colour
Blue 15 5 20
Grey 20 10 20
Brown 25 15 20
when we in the united states says a car's tire is filled "to 32 lb," we mean that its internal pressure is 32 lbf/in^2 above the ambient atmosphere. if the tire is at sea level, has a volume of 3.0 ft^3, and is at 75 degree fahrenheit, estimate the total weight of air, in lbf, inside the tire.
Find the final weight, volume and pressure of the gas.
what is the difference between chemistry and chemical engineering
Continuous cable ADB runs over a small frictionless pulley at D to support beam OABC which is part of an entrance canopy for a building (see figure 3). A downward distributed load with peak intensity q0 = 5 kN/m at O acts on the beam. Assume that canopy weight W = 8 kN and that cable cross-sectional area is 100 mm2 . a) Find cable force T and pin support reactions at O and D b) Find the normal stress in the cable in the cable ADB c) Determine the required diameter of pins A, B, D and O if the pins are in double shear and the allowable shear stress is 80 MPa? Note that OA = AB = BC = 1.5m.
what is the sequence in the making of Extreme Constructions The Meraviglia Cruise Ship. A magnetic stirrer agitated vessel is used for absorption of CO2 in water at 298 K and 2
atm pressure. Water is fed at a rate of 1 L/min and the carbonated water leaves the vessel
continuously so that a constant volume is maintained in the contactor. The outlet water
contains 2.3 g CO2/L. The interfacial area of gas-liquid contact is 80 m2
/ m3
; the volume of
gas-liquid dispersion is 8 L. The solubility of CO2 in water can be found using Henry’s law.
At 298 K, the Henry’s law constant for CO2 is 1640 atm/mole fraction and it’s diffusivity in
water is 1.92 x 10-9 m/s. The density of liquid is 997 kg/ m3
. Calculate:
(i) The thickness of the liquid film, if the Film theory is applicable.
(ii) The contact time between the liquid element with the gas if the Penetration theory is
applicable.
(iii) The surface renewal rate if the Surface-renwal theory is applicable. (
For the absorption of dilute gas mixture in a packed column, derive that
y y lm
y y
N
e
toG
1 2