As point 1 and point 2 are arbitrarily chosen on a streamline so p+=pv=const Along a streamline As there are no stipulation being made to whether the flow is rotational or irrotational it satisfies for both irrotational flows and rotational flows as well 2. The value of the constant will change from one streamline to another 3. For irrotational flows p+pv=const Through out the flow 2
As point 1 and point 2 are arbitrarily chosen on a streamline, so p + V = const 2 2 1 Along a streamline 1. As there are no stipulation being made to whether the flow is rotational or irrotational, it satisfies for both irrotational flows and rotational flows as well. 2. The value of the constant will change from one streamline to another. 3. For irrotational flows p + V = const 2 2 1 Through out the flow
o Bernoullis equation is also a relation for mechanical energy in an Incompressible flow p+=p V= const where pv2 /2 is the kinetic energy per unit volume As Bernoulli's equation can also be derived from the energy equation, the energy equation is redundant for the analysis of inviscid incompressible flow
Bernoulli’s equation is also a relation for mechanical energy in an incompressible flow p + V = const 2 2 1 where is the kinetic energy per unit volume 2 2 V As Bernoulli’s equation can also be derived from the energy equation, the energy equation is redundant for the analysis of inviscid, incompressible flow
The way for solving inviscid, incompressible flows 1, Obtain the velocity field from the governing equations. 2. Obtain the pressure field from Bernoullis equation
The way for solving inviscid, incompressible flows: 1. Obtain the velocity field from the governing equations. 2. Obtain the pressure field from Bernoulli’s equation
3.3 Incompressible flow in a duct: the Venturi tube and low-speed wind tunnel
3.3 Incompressible flow in a duct: the Venturi tube and low-speed wind tunnel
Assumption of quasi-one-dimensional flows 1. Flow-field properties are uniform across any cross seCo门 2. Al// the flow-field properties are assumed to be functions of X only o Respect to continuity equation, and for steady case 141+P2A2V2=0 O厂 PA=p2Ay2
Assumption of quasi-one-dimensional flows 1. Flow-field properties are uniform across any cross section. 2. All the flow-field properties are assumed to be functions of x only. Respect to continuity equation, and for steady case − 1 A1 V1 + 2 A2 V2 = 0 or 1 A1 V1 = 2 A2 V2