We have derived a general balance equation applicable to mass, momentum and energy in the form pfdv=-fpfunds- nds + [ f pedV+ $ Apply this equation to the flow in a cylindrical tube of diameter d and cross-sectional area A and ta as the control volume V appearing in the equation an infinitesimal "slice" of tube of thickness da (t coordinate z varies in the direction of the axis of the tube). Note that d (2+) --Jz+dzdA-b--]zdA = dz & gl..JdA da (z+dx) A(z) After deriving the general form of the equation, apply it to the statements of conservation of ma momentum along the tube axis, and energy. Show that, neglecting qr and Trr, for fully-develop time-independent flow, the momentum and energy equations give Tw= 1 op 4 x' onds. and Pqwall. "Fully developed" means that the velocity does not depend on z; Tis the relevant component the viscous stress at the tube wall and quall is the relevant component of the heat flux vector (bo assumed constant over the tube wall); P is the perimeter of the tube. The overline denotes the avera over the tube cross section; for example P = pdA.