Bernoulli's Theorem 1
Bernoulli's Theorem 1 : As originally formulated, a statement of the conservation of energy (per unit mass) for a non-viscous fluid in steady motion, the specific energy is composed of the kinetic energy v2/^ where v is the speed of the fluid; the potential energy gz where g is the acceleration of gravity and z the height above an arbitrary reference level; and the work done by the pressure forces j adp where p is the pressure, a the specific volume, and the integration is always with respect to values of p and a on the same parcel. Thus, the relationship [ adp-constant along a streamline, = is valid for steady motion, since the streamline is also the path. If the motion is also irrotational, the same constant holds for the entire fluid. The following special cares are important: (a) as originally formulated for a homogeneous incompressible fluid, / adp = ap ; and (b) for a perfect gas undergoing adiabatic processes, j adp = cpT where cp is the specific heat at constant pressure and T the Kelvin temperature. If there is diabatic heating on the parcel at the rate dQ/dt per unit mass, then !adp = cpT-UQ. (Prandll, L., Essentials of Fluid Dynamics, 1952, Ch. H, passim. Haurwitz, B., Dynamic meteorology, 1941, pp. 238-241)
No records Found