1, flow continuity equation:
The flow continuity equation is based on the law of conservation of mass, which shows that in a closed system, the mass of fluid will not be produced or disappeared out of thin air. Mathematically, this can be expressed as: inflow mass flow = outflow mass flow or, in mathematical notation: ρ/kloc-0 /× a/kloc-0 /× v1= ρ 2× a2× v2.
2, Bernoulli equation:
Bernoulli equation is based on the law of conservation of energy, which shows that in incompressible inviscid fluid, the total energy of the fluid (including kinetic energy, potential energy and pressure energy) is constant along a streamline. Mathematically, this can be expressed as: p1+1/2× ρ× v12+ρ g× h1= p2+1/2×ρ× v2 2+ρ× g×.
Where p is pressure, ρ is fluid density, v is flow velocity, g is gravity acceleration, and h is height. Now we have to solve this problem and verify these two equations through concrete numerical calculation.
The solution of flow continuity equation is [{a1:a2v2rho2/(v1rho1)}] The solution of Bernoulli equation is [{P 1: P2-0.5V 1 _ squared rho+0.5v].
It should be noted that these two equations are theoretical models and are usually used to analyze and design fluid systems. In practical application, other factors such as viscosity and compressibility need to be considered.
The application conditions of Bernoulli equation include: the fluid is inviscid and incompressible, and the total energy along the streamline is constant. The flow continuity equation is based on the law of conservation of mass, which emphasizes that the mass of fluid will not appear or disappear out of thin air during the flow. These two equations have important applications in fluid mechanics, but the physical principles and conditions behind them are different.