伯努利定律

伯努利定律 In a fluid system, such as air, water, faster flow generated by the fluid pressure is smaller, which is called "Bernoulli's law of fluid mechanics" father of Daniel Bernoulli "discovered in 1738". The force of this pressure is enormous. Air can lift heavy airplanes, using Bernoulli's law. The upper surface of an aircraft wing is a smooth surface, while the lower surface is flat. In this way, the airflow on the upper surface of the wing is faster than the air velocity at the lower surface, so the pressure on the air below the wing is greater than the pressure of the upper air, and the aircraft is held up by this great pressure difference In a fluid system, such as air, water, faster flow generated by the fluid pressure is smaller, which is called "Bernoulli's law of fluid mechanics" father of Daniel Bernoulli "discovered in 1738". The force of this pressure is enormous. Air can lift heavy airplanes, using Bernoulli's law. The upper surface of an aircraft wing is a smooth surface, while the lower surface is flat. In this way, the airflow on the upper surface of the wing is faster than the air velocity at the lower surface, so the pressure on the air below the wing is greater than the pressure of the upper air, and the aircraft is held up by this great pressure difference. Of course, how big is the pressure? An advanced fluid mechanics formula, the Bernoulli equation, will calculate it. Edit this paragraph equation V= flow velocity g= geocentric acceleration (earth) Bernoulli's law H= fluid in height (from a reference point gauge pressure P = p=) fluid fluid by density Edit this paragraph of the law hypothesis 1. non viscous fluid without viscous force between resistance and the vessel wall 2. incompressible gas due to the compressibility of many do not follow the law; not compressibility can maintain constant density 3. stable high-speed flow will lead to turbulence Edit this paragraph inference process 设在右图的细管中有理想流体在做定常流动,且流动方向从左向右, 我们在管的a1处和a2处用横截面截出一段流体,即a1处和a2处之 间的流体,作为研究对象.设a1处的横截面积为S1,流速为V1,高度为 h1;a2处的横截面积为S2,流速为V2,高度为h2. 如图所示,经过很短 的时间Δt,这段流体的左端S1由a1移到b1,右端S2由a2移到b2, 两端移动的距离为ΔL1和ΔL2,左端流入的流体体积为ΔV1=S1ΔL1, 右端流出的体积为ΔV2=S2ΔL2. 因为理想流体是不可压缩的,所以 有 ΔV1=ΔV2=ΔV 作用于左端的力F1=p1S2对流体做的功为 W1=F1ΔL1=p1?S1ΔL1=p1ΔV 作用于右端的力F2=p2S2,它对流体做 负功(因为右边对这段流体的作用 This force to the left, and the fluid displacement to the right), the work done for W2=-F2 Delta L2=-p2S2 Delta L2=-p2 Delta V on both sides of the forces acting on the liquid total work for W=W1+W2= (P1-P2) V and because we are the ideal fluid unsteady flow, fluid density and velocity of each point V did So the research object (the initial state is A1 to A2 between the final fluid, is B1 to B2 between the fluid) and gravity energy has not changed. So, the change of mechanical energy is equal to that part of the mechanical energy of the fluid outflow minus the inflow portion of the fluid mechanical energy, namely E2-E1= (P V+). P g (h2-h1) V and not ideal fluid viscosity, the fluid flow in the machine can not be transformed into energy star W=E2-E1 (P1-P2) V= (P -)) V+ p g (h2-h1) V after finishing: after finishing: A1 and A2 are in fluid taken. So can the table for the two type is the Bernoulli equation. When the fluid flow level, or height is not significantly affected, the Bernoulli equation can be expressed as the meaning of the formula is: in fluid flow, pressure and flow rate, flow rate of V large local pressure P, flow rate V small place the pressure of P. Edit this paragraph history Bernoulli developed and named the discipline of fluid dynamics, distinguishing the different concepts of fluid statics and dynamics. In 1738, he published the "fluid dynamics" bided written a book. He used the fluid pressure, density and velocity as the basic concept description of fluid motion, introduced the "potential function" of "potential energy" ("potential improvement") instead of simply using "dynamic" discussion, so as to express the Bernoulli equation for ideal fluid flow, this substance is a mechanical energy the form of conservation law. He also explained the gas pressure by colliding molecules with the wall, and pointed out that, as long as the temperature is constant, the pressure of the gas is always positively proportional to the density, and inversely proportional to the volume. This explains Boyle's law. Edit this section of Bernoulli equation 设在右图的细管中有理想流体在做定常流动,且流动方向从左向右, 我们在管的a1处和a2处用横截面截出一段流体,即a1处和a2处之 间的流体,作为研究对象.设a1处的横截面积为S1,流速为V1,高度为 h1;a2处的横截面积为S2,流速为V2,高度为h2. 思考下列问题: ?a1处左边的流体对研究对象的压力F1的大小及方向如何 ?a2处 右边的液体对研究对象的压力F2的大小及方向如何 ?设经过一段 时间Δt后(Δt很小),这段流体的左端S1由a1移到b1,右端S2由 a2移到b2,两端移动的距离分别为ΔL1和ΔL2,则左端流入的流体 体积和右端流出的液体体积各为多大 它们之间有什么关系 为什么 ?求左右两 The research object of power machinery end force on the selected research object can do is changed and why liquid in the flow process, the external force to do work on it, combined with the functional relationship, the work of the external forces and fluid machinery can change what is the relationship between the derivation process: as shown, after a very short this period of time was t, the left S1 fluid by the shift from A1 to B1, the right end of S2 by the shift from A2 to B2, both ends of the moving distance is L1 and L2, the volume of fluid into the left for Delta V1=S1 Delta L1, right outflow volume of delta V2=S2 Delta L2. because the ideal fluid is incompressible So there is a delta V1= Delta V2= Delta V to the left of the work fluid force F1=p1S2 W1=F1 L1 =p1 S1 L1=p1 Delta Delta Delta V acting on the right end of the F2=p2S2, it does negative work on fluid (because the left, on the right of the fluid force and the fluid displacement to the right). The work done for the W2= -F2 Delta L2=-p2S2 Delta L2=-p2 Delta V on both sides of the forces acting on the liquid total work for W=W1+W2= (P1-P2) V and because we are the ideal fluid unsteady flow, fluid density and the flow rate of V has not changed, so the research object (initial state is A1 to flow, A2 between States is B1 to B2 between the fluid) and gravity energy has not changed. So, the change of mechanical energy is equal to that part of the mechanical energy of the fluid outflow minus the inflow portion of the fluid mechanical energy, namely E2-E1= (P) V+ p g (h2-h1). V ideal No viscosity fluid, the fluid flow in the machine can not be transformed into energy star W=E2-E1 (P1-P2) V= (P -)) V+ p g (h2-h1) V after finishing: after finishing: A1 and A2 are in fluid taken, so the formula can be expressed as the type two is Bernoulli equation. When the fluid flows horizontally or when the height is not significant, the Bernoulli equation can be expressed as the meaning of the equation: flow in the fluid