The incompressible laminar fluid flows inside a horizontal capillary tube of radius R. The pressure difference is measured using a monometer filled with liquid CCl4. Length of capillary tube L:50.02cm; Kinematic viscosity of liquid =/:4.03105m2s1; Density of fluid :0.9552103kgm3; Density of CCl4C : 1.59103kgm3 In the monometer, h=7.76cm Mass flow rate of fluid through tube w: 2.997103kgs1 g is referred to the acceleration of gravity. (a) Derive fluid velocity vz distribution in the capillary tube: vz=4L(CCl4)hgR2[1(Rr)2]. [20 marks] (b) When the pressure drop in the horizontal tube is measured by the CCl4 column difference h in the monometer, estimate the capillary radius. [hint: according to the Vz distribution function to derive the mass flow rate equation that contains the R ] [20 marks] (c) Calculate the maximum velocity. [20 marks] (d) Calculate the average velocity. [20 marks] (e) Calculate the force exerted on tube inner surface by fluid. [20 marks] Newton's law of viscosity Cylindrical coordinates (r,,z) : =[2rvr]+(42)(v)=[2(r1ve+rvv)]+(72)(v)zz=[2zti]+(3)(v)r=+=[r(rv)+r1vt]z=zy=[r1vz+zvf]zr=ru=[zv+rvz] in which (v)=r1r(rvn)+r1v+zvr