L 2 .d.x x=0 Find the velocity distribution of an inviscid fluid flowing through the tube shown in Figure 1.8(a). The differential equation governing the velocity distribution u(x) is given by Eq. (1.12) with the boundary condition u(x = 0) = Uo. This problem is equivalent to 22 please answer with all steps 1 do Minimize I = pA dx (E.1) with the boundary condition u(x = 0) = 10 where $(x) is the potential function that gives the velocity of the fluid, u(x), as u(x) = dp(x)/dx. Assume the area of cross-section of the tube as A(x) = Ao-e-(x/L). Note The variation of the potential funcion along the tube (i.e., the solution of the problem) can be found either by solving the governing differential Eq. (1.12) using the given boundary condition, or by minimizing or extremizing the functional I using the given boundary condition. The functional I is used in this example to illustrate the method of deriving the element matrices and element load vectors using a variational principle. Although the functional I has no physical meaning it is similar to the potential energy functional used for stress analysis (in Example 1.2)