The Continuity Equation with Incompressible Fluid equation solved for area calculates the cross-sectional area of an incompressible fluid with an escape velocity given and the second end of the tube's escape velocity and cross-sectional area.
Young, Hugh and Freeman, Roger. University Physics With Modern Physics. Addison-Wesley, 2008. 12th Edition, (ISBN-13: 978-0321500625 ISBN-10: 0321500628 ) Pg 467, eq 14.10