What is Bernoulli s Equation? What is Bernoulli s equation?

Definition: An equation that reflects the relationship between parameters such as velocity, pressure, etc., in the motion of an ideal fluid.

Bernoulli's equation is a dynamic equation for the steady flow of an ideal fluid, which means that the sum of the pressure potential energy, kinetic energy and potential energy at any two points on the streamline remains unchanged in the flow of the fluid ignoring viscous loss.

The equation is p + gh + (1 2) * v 2 = c where p, and v are the pressure, density, and velocity of the fluid, respectively; h is the plumb height; g is the acceleration due to gravity; c is a constant. Supplement: p1+1 2 v1 2+ gh1=p2+1 2 v2 2+ gh2(1) p+ gh+(1 2)* v2=constant (2) are Bernoulli's equations.

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Bernoulli's equation is an important basic equation in fluid mechanics, and the study of fluids should not only know the relationship between flow velocity and cross-section, but also further understand the relationship between flow velocity and pressure of fluids.

Daniel Bernoulli proposed the "Bernoulli Principle" in 1726. This is the basic principle adopted by hydraulics before the establishment of the theoretical equations of continuum in fluid mechanics, the essence of which is the conservation of mechanical energy of fluids. Namely:

Kinetic energy, gravitational potential energy, pressure potential energy, constant. The most famous corollary is that when the flow is at a constant height, the flow velocity is high, and the pressure is small.

It is important to note that since Bernoulli's equation is derived from the conservation of mechanical energy, it is only suitable for ideal fluids with negligible viscosity and non-compressibility.

Assumptions of Bernoulli's equation:The use of Bernoulli's law must meet the following assumptions before it can be used; If the following assumptions are not fully met, the solution is also approximate.

1. Steady flow: In the flow system, the properties of the fluid at any point do not change with time.

2. Incompressible flow: the density is constant, and the fluid is a gas and is suitable for Mach number (ma) <.

3. Frictionless flow: the friction effect can be ignored, and the viscous effect can be ignored.

4. Fluid flows along the streamline: The fluid elements flow along the streamline, and the streamlines do not intersect each other.

Bernoulli's equation is indeed derived from the conservation of mechanical energy, which is the embodiment of the conservation of energy in fluid mechanics

However, it must be noted that the left side of this equation is not an expression of energy, but the volume is removed, which means that the meaning of this equation is: the conservation of mechanical energy per unit volume.

Energy per unit volume, defined as energy density, is a quantity of intensity, so it has nothing to do with the amount of liquid flowing.

If (1-1), (2-2), and (3-3) denote the mechanical energy densities of the three pipes respectively (i.e., the equation on the left side of Bernoulli's equation), then of course (1-1) = (2-2) = (3-3).

Suppose we can measure the volumes v1, v2, and v3 of the three pipes flowing through the cross-section per unit time, then we can get it.

v1(1-1)=v2(2-2)+v3(3-3),You can get v1=v2+v3 after the appointment,This is the answer you want!!

Bernoulli's equation for fluid mechanics is p+1 2 v2 + gh=c.

p is the pressure at a point in the fluid, v is the velocity of the fluid at that point, is the density of the fluid, g is the acceleration due to gravity, h is the height at the point, and c is a constant.

It can also be expressed as p1+1 2 v12+ gh1=p2+1 2 v22+ gh2.

Bernoulli's equation is the fundamental equation that describes the conservation of energy in the course of the motion of an ideal fluid along a streamline. The equation is named after the Swiss physicist Daniel Bernoulli, who first proposed the principle.

Bernoulli's equation can be expressed as:

p + 1/2ρv^2 + gh = constant

Where: p is the static pressure of the fluid (in pascal), is the density of the fluid (in kilograms and cubic meters), v is the velocity of the fluid (in meters and seconds), g is the acceleration due to gravity (in meters and seconds), and h is the height of the fluid (in meters).

Bernoulli's equation shows that in the absence of work done by external forces and energy loss, the sum of the static pressure, dynamic pressure (i.e., quantification of kinetic energy) and gravitational potential energy remains constant when an ideal fluid moves along a streamline.

Bernoulli's equation has a wide range of applications in fluid mechanics. For example, it can be used to analyze the relationship between the flow rate, pressure, and altitude of a pipeline fluid, to explain how lift is generated in an aircraft, and to understand phenomena such as fluid motion in rivers, dams, or turbines. It is important to note that Bernoulli's equation only applies to ideal fluids, i.e., fluids that do not have non-ideal luge segments such as viscosity and turbulence.

Bernoulli's equation is an equation in fluid mechanics that describes the conservation of energy in the direction of flow. It is suitable for situations where steady-state, incompressible, non-viscous fluids are in the flow process. Bernoulli's equation can be expressed by the following formula:

p + 1 2 * v 2 + g * h = constant where p is the static pressure (pressure) of the fluid;

is the density of the fluid;

v is the flow rate (velocity) of the fluid;

g is the acceleration due to gravity;

h is the height (elevation) of the fluid.

This formula expresses that in steady-state flow, the total energy between any two points along the streamline remains constant. Three of them represent static pressure energy, dynamic pressure energy, and gravitational potential energy, respectively. In the absence of viscous, incompressible fluids, Bernoulli's equations have great applications in explaining problems such as flight, liquid flow, and water flow.

It is important to note that Bernoulli's equation is derived by ignoring some factors, such as the loss of viscocius, compressibility effects, and eddy currents. In some cases, these factors can have a significant impact on the behavior of the fluid, so more complex equations or models may be required to describe the behavior of the fluid in a particular problem.

Bernoulli's equation: p+ gz+(1 2)* v 2=c, where p, , and v are the pressure, density, and velocity of the fluid, respectively; h is the plumb height; g is the acceleration due to gravity; c is a constant.

A straightforward conclusion is that the pressure is low at high flow rates and high at low flow rates.