Reactor core flow cross-section is equal to 5m 2.Flow velocity in the cold leg is equal to 17 m/s.Primary piping flow cross-section (single loop) is equal to 0.385 m 2 (piping diameter ~ 700mm).Fluid of constant density ⍴ ~ 720 kg/m 3 (at 290☌) is flowing steadily through the cold leg and through the core bottom.For a control volume that has a single inlet and a single outlet, the principle of conservation of mass states that, for steady-state flow, the mass flow rate into the volume must equal the mass flow rate out.ĭetermine pressure and velocity within a cold leg of primary piping and determine pressure and velocity at a bottom of a reactor core, which is about 5 meters below the cold leg of primary piping. The continuity equation is simply a mathematical expression of the principle of conservation of mass. When the Bernoulli’s equation is combined with the continuity equation the two can be used to find velocities and pressures at points in the flow connected by a streamline. It is an illustrative example, data do not represent any reactor design. It is an illustrative example, following data do not correspond to any reactor design. The dimensions of terms in the equation are kinetic energy per unit volume.īernoulli’s Effect – Relation between Pressure and Velocity In the high velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy. This lowering of pressure in a constriction of a flow path may seem counterintuitive, but seems less so when you consider pressure to be energy density. This effect causes the lowering of fluid pressure in regions where the flow velocity is increased. The Bernoulli’s equation describes the qualitative behavior flowing fluid that is usually labeled with the term Bernoulli’s effect. This equation is the most famous equation in fluid dynamics. Under these conditions, the general energy equation is simplified to: the equation relates the states at two points along a single streamline (not conditions on two different streamlines).no change occurs in the internal energy,.no heat is transferred to or from the fluid,.density is constant (which also means the fluid is incompressible),.Bernoulli’s equation has some restrictions in its applicability, they summarized in following points: It puts into a relation pressure and velocity in an inviscid incompressible flow.

It is one of the most important/useful equations in fluid mechanics. The Bernoulli’s equation can be considered to be a statement of the conservation of energy principle appropriate for flowing fluids.

Bernoulli principle gases