By H. R. Vallentine (auth.)
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Additional resources for Applied Hydrodynamics
X) .... p- i(x'-y 1 ) +a constant, satisfies both (a) and (b). p - constant. 21. 5. Show that the two-dimensional irrotational flow stream function rp = u(r- ~) sin 8 represents the pattern of steady flow in the x-direction, past a cylinder of radius a, of an infinite fluid whose undisturbed velocity is U. Determine the potential function and find the distribution of velocity on the boundary of the cylinder. 22). The other streamlines plot as shown. Streamlines inside the circle can have no influence on the pattern outside the circle and this circle can be regarded therefore as the solid boundary of a cylinder of radius a, lying acroSs the flow.
This is a mathematical device which is analogous to the velocity potential, for it is a function of x, y and z such that, when differentiated with respect to distance in any given direction it yields minus the component of gravity force per unit mass in that direction. If the direction vertically upward, that is, opposite to the direction of gravity, is represented by the h-axis, then the potential energy or force potential, with respect to some selected datum level, of unit 37 FLOW OF AN IDEAL FLUID mass at a height h above datum, is n= ....
1s zero. V2+gh+e p = C' or 40 .... 39) VELOCITY AND PRESSURE DISTRIBUTIONS which is the restricted form of the Bernoulli equation, relating to points on any one streamline in steady flow of a non-viscous incompressible fluid. _ and h, have the dimeng y sions of energy per unit weight of fluid, for example, foot pounds per pound weight or, simply, feet. In fact, :; is the kinetic energy per pound and his the gravitational potential energy per pound referred to some datum level. The pressure term, does not represent, in y itself, a pressure energy content per unit weight of fluid.
Applied Hydrodynamics by H. R. Vallentine (auth.)