# What is Bernoulli equation: Definition and 130 Discussions

In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler who derived Bernoulli's equation in its usual form in 1752. The principle is only applicable for isentropic flows: when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g. heat radiation) are small and can be neglected.
Bernoulli's principle can be applied to various types of fluid flow, resulting in various forms of Bernoulli's equation. The simple form of Bernoulli's equation is valid for incompressible flows (e.g. most liquid flows and gases moving at low Mach number). More advanced forms may be applied to compressible flows at higher Mach numbers (see the derivations of the Bernoulli equation).
Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy, potential energy and internal energy remains constant. Thus an increase in the speed of the fluid – implying an increase in its kinetic energy (dynamic pressure) – occurs with a simultaneous decrease in (the sum of) its potential energy (including the static pressure) and internal energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρ g h) is the same everywhere.Bernoulli's principle can also be derived directly from Isaac Newton's Second Law of Motion. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline.Fluid particles are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest.

View More On Wikipedia.org
1. ### Bernoulli equation for calculation of water flow

Hello everyone; Please need some help to check if my calculation are correct (and if possible some explantation) Bernoulli's equation between point 1 and 3 is given by: P_1+1/2 ρv_1^2 + ρgh_1 = P_3+1/2 ρv_3^2 + ρgh_3 P_1 = P_(atm ) v_1= 0 m/s h_1= 0.875 m P_3 = P_(atm ) v_3= ? m/s h_3= 0...
2. ### Can you please explain Bernoulli's equation?

Can you please explain why is there work done by F2(on photo of textbook explanation of Bernoully equation (photo below)). I can understand that W2 is caused by F2 which is gravitational force(screenshot photo from YT). But for the explanation in textbook pipe is straight, no height...

45. ### Bernoulli Equation and Velocities

Homework Statement A cubic wine box of dimensional length ##h## has a small tap at an angle at the bottom. When the box is full and is lying on a horizontal plane with the tap open, the wine comes out with a speed ##v_0##. i) What is the speed of the wine if the box is half empty? (Neglect...
46. ### Why is Bernoulli's Equation Isentropic

I have trouble understanding why we classify an inviscid adiabatic incompressible flow along a streamline as isentropic I understand this from a Thermodynamic definition/explanation $$dS = dQ/T$$ Adiabatic Invsicid $$dQ =0= dS$$ So no heat added or lost no change in entropy I'm fine with that...
47. ### Evaluate Problems using fluid dynamics

I have a diagram similar to the following. Water entering the larger end is at 20degreesC. The larger end has a diameter of 8cm and Area 50.26cm2. The small side has a diameter of 3cm and Area 7.0685cm2. The water jet exerts a force of 87N on a flat plate at an unknown distance. Assuming no...
48. ### How to solve using Bernoulli equation

Homework Statement What gauge pressure is required by city mains for a stream from a fire hose connected to the mains to reach a vertical height of 15m? Homework Equations Bernoulli Equation: The Attempt at a Solution
49. ### Bernoulli Equation and Leakage in a Pipe

Hi boneh3ad Your discussion on Bernoulli Equation was very impressive and helped me a lot to understand this rather complicated equation. I have a question which puzzles me a lot when I want to solve it using Bernoulli equation. Here is the statement. " If there is some fluid flowing thru a...
50. M

### Bernoulli Equation and Navier-Stokes

Hi PF! I was reading about Bernoulli's equation for steady, inviscid, incompressible flow. Now it's my understanding this equation is derived from the Navier-Stokes (momentum balance); then these two equations are identical regarding information offered. However, while thinking about...