ABSTRACT
If the limits of integration are variable, as illustrated in Figure 6.10, that must be accounted for.
Example 6.7. Double integral
To illustrate double integration with variable limits of integration, let's calculate the mass of water in a cylindrical container which is rotating at a constant angular velocity ill, as illustrated in Figure 6.11 a. A meridional plane view through the axis of rotation is presented in Figure 6.11 b. From a basic fluid mechanics analysis, it can be shown that the shape of the free surface is given by
z(r) = A + Br2 (6.100) From measured data, z(O) = ZI and z(R) = Z2' Substituting these values into Eq. (6.100) gives
(6.101)
