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Express each of the following dimensionless numbers in terms of density , heat capacity Cp, viscosity , thermal conductivity k, diffusion coefficient DAB, velocity v, and diameter d. Use only one sentence to describe the meaning of each dimensionless group. i) Reynolds number ii) Prandtl number iii) Schmidt number Consider the steady-state absorption of pure component gas A in a liquid solvent composed of B as shown by the schematic in Figure 1. When dissolved in the liquid, A undergoes an irreversible first order reaction A+BC. The kinetics are described by a first-order rate equation rA=kcA where k is a rate constant, rA is the rate of reaction, and cA is the concentration of A in the liquid. The concentration profile is given by cA=cA0cosh[(z)/l]/cosh(/l) where l2=DAB/k,DAB is the diffusion coefficient for A in B,cA0 is the concentration of A at the gas-liquid interface, and is the thickness of the liquid film. Figure 1: Absorption of A from gas phase into a liquid solvent composed of B. In the solvent, A reacts with B to form C. i) Explain the meaning of the dimensionless group /l. ii) Determine the flux of A at the gas-liquid interface, NA,zz=0. iii) Calculate the average rate of reaction rA,avg=kcA,avg where cA,avg is the average concentration of A in the liquid film. iv) Show that the average rate of reaction can also be calculated from the expression for NA,zz=0 derived in part (ii) above. v) Determine NA,zz=0 in the limit of /l0. Explain the physical meaning of the result. Components of the stress tensor for a Newtonian fluid in spherical coordinates rr=[2rvr32(v)]=[2(r1v+rvr)32(v)]=[2(rsin1v+rvr+rvcot)32(v)]r==[rr(rv)+r1vr]==[rsin(sinv)+rsin1v]=r=[rsin1vr+rr(rv)] Components of the stress tensor for a Newtonian fluid in cylindrical coordinates rr=[2rvr32(v)]=[2(r1v+rvr)32(v)]zz=[2zvz32(v)]r=r=[rr(rv)+r1vr]z=z=[zv+r1vz]zr=rz=[rvz+zvr] Components of the stress tensor for a Newtonian fluid in rectangular coordinates xx=[2xvx32(v)]yy=[2yvy32(v)]zz=[2zvz32(v)]xy=yx=[yvx+xvy]yz=zy=[zvy+yvz]zx=xz=[xvz+zvx] Equation of motion in spherical coordinates for a Newtonian fluid with constant and . r-component (tvr+vrrvr+rvvr+rsinvvrrv2+v2)=rp+[r21r22(r2vr)+r2sin1(sinvr)+r2sin2122vr]+gr -component (tv+vrrv+rvv+rsinvv+rvrvrv2cot)=r1p+[r21r(r2rv)+r21(sin1(vsin))+r2sin2122v+r22vrr2sin22cosv]+g -component (tv+vrrv+rvv+rsinvv+rvvr+rvvcot)=rsin1p+[r21r(r2rv)+r21(sin1(vsin))+r2sin2122v+r2sin2vr+r2sin22cosv]+g Equation of motion in cylindrical coordinates for a Newtonian fluid with constant and . r-component (tvr+vrrvr+rvvrrv2+vzzvr)=rp+[r(r1r(rvr))+r2122vrr22v+z22vr]+gr -component (tv+vrrv+rvv+rvrv+vzzv)=r1p+[r(r1r(rv))+r2122v+r22vr+z22v]+gz-component(tvz+vrrvz+rvvz+vzzvz)=zp+[r1r(rrvz)+r2122vz+z22vz]+gz Equation of motion in rectangular coordinates for a Newtonian fluid with constant and : x-component (tvx+vxxvx+vyyvx+vzzvx)=xp+(x22vx+y22vx+z22vx)+gx y-component (tvy+vxxvy+vyyvy+vzzvy)=yp+(x22vy+y22vy+z22vy)+gy z-component (tvz+vxxvz+vyyvz+vzzvz)=zp+(x22vz+y22vz+z22vz)+gz