What is Bernoulli equation: Definition and 133 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.
I’ve been confused about the term static pressure for quite some time. Different sources use very different definitions. From the problems perspective, it’s usually some external pressure. For example we are having a pool with tiny hole on the bottom which makes water level decrease and it flows...
Hi,
I am trying to map out the forces that act on a raincap installed at the end of a pipe, but I have ran into a problem where I am getting 2 different equations depending on the method that I use. I'm definitely missing something here and I was hoping someone is about to point it out to me...
There is a classical example when teaching Bernoulli equations to get the exit velocity of a fluid leaving through the bottom of a tank. If we consider no energy is lost due to friction, the exit velocity turns out to be ##v=\sqrt {2gh}##. I'm having trouble processing the fact that exit speed...
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...
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...
I was looking at an example of fluid mechanics and I don't understand this.
Statement figures:
CONTINUITY EQUATION
$$\left. \dfrac{dm}{dt}\right]_{MC}=(\dot{m}_2+\dot{m}_3)-\dot{m}_1=0$$
$$\dot{m}_1=\dot{m}_2+\dot{m}_3$$
$$\rho c_1A_1=\rho c_2A_2+\rho c_3A_3$$
$$\rho c_1 h1=\rho c_2 a1+\rho...
Hello!
I have a question regarding the application of the bernoulli equation and calculation of the flow through a parallel pipe branch. It's more the basic understanding how the flow will establish.
You can find a sketch attached to follow my explanation.
Let's assume I have a pipe with...
Hi, everyone! Doing some fluid flow/Bernoulli tasks.
Ok, so the task is:
«A hose with a radius of 0,035m is connected to a nozzle, which reduces the radius of the hose to 0,018m (2). The hose carries (qv) 0,0075 m3/sec and the totalpressure (3) in the wide section (1) is 211 kPA. The density of...
Good afternoon,
I am struggling to find the solution at Q2 and Q3. For Q2 the absolute pressure at point 1 is at the bottom of the tank, so do i need to use the formula P=Patm+qgh ? If using this formula I've got a bigger number than 100Pa.
Same issue for Q3, isn't the pressure at point 2...
Hey all,
I recently took an aerodynamics exam that included the question "Please Explain how the Bernoulli Equation can be Applied Inside a Boundary Layer". Now, it is my belief that the Bernoulli equation, defined by my textbook as P+0.5ρV2=ℂ, requires inviscid flow to be properly applied...
Hi, I´m quite lost and would appreciate guidance
I have solved for 2 tubes using Bernoulli´s equation before, but now how does it change?
Is it really going to rise water level inside? Why?
In classical and continuum mechanics if we want to find equation of motion of the body we draw force diagram and apply Newton's 2nd law.
In continuum mechanics, equation of motion actually refers to a special point of the body known as center of mass (COM) which can be proven by definition of...
Work - energy principle states that work done by net force acting on the body equals change in kinetic energy of the body. We are talking about continuum mechanics. This principle is usually introduced in mechanics of solid bodies. For us to describe the motion of the body, it is enough to know...
Work - Energy principle states that work of resultant force or sum of work of all forces acting on some system equals change in kinetic energy of the system.
For inviscid fluid flowing in a pipe such theorem can be used to derive Bernoulli's equation because as fluid flows it is subjected to...
I have read this in my textbook about principles of operation of centrifugal compressor:
"The impeller is rotated at high speed by the turbine and air is continuously induced into the center of the impeller. Centrifugal action causes it to flow radially outwards along the vanes to the impeller...
For a steady, non-viscous and incompressible flow, one can apply both Bernoulli's principle (no potentials) as
$$p+\frac{\rho v^2}{2} = p_t$$
where ##p##, ##\rho,##, ##v##, and ##p_t## are static pressure, density, flow velocity, and total pressure, respectively,
and continuitiy principle as...
I am trying to calculate the exit velocity of a nozzle (0,25Ø) that is connected to a high pressure syringe (10 BAR), however I cannot understand why Hagen-Poiseuille will have a higher exit velocity then Bernoulli when HP take viscosity into account.
Hi there, I'm doing a past exam paper Q and i'd like some help.
Assumptions are: The velocity in the tank is negligible and the hydrostatic head is 4m.
Pressure in the vessel:
Gauge pressure
1 bar g = 10^5 Pa
0.2 bar g = 20,000 Pa
Hydrostatic Pressure: (4)(9.81)(978) = 38,376.72 Pa
Absolute...
Let's start with a horizontal tube with a constant diameter. I'm not sure if it's important, but let's assume it's frictionless. I will have some fluid flowing in this tube and if it's important, we can make the fluid incompressible, inviscid, irrotational, etc.
To create a flow in the tube...
Hi all!
This is my first post here, so hopefully I am not in violation of any rules or etiquette. I'm looking to derive an equation for Reynolds number as function of pressure for a pinhole leak in a pressurized gas line. The line is regular air and is pressurized to 1 atmosphere and is leaking...
Here i added a page from my fluid dynamics book where it shows particle model for deriving the equation. My question is why pressure is more at stream side aka 'positive "s" direction'.I would expected more pressure on the other side because for example when you trying to push a rigid object or...
Elemental fixed streamtube control volume from Professor White’s textbook “Fuid Mechanics”:
I was unable to develop the intermediate steps for the following approximations:
(continuity equation according to the book )
Where
and
(Momentum equation according to the book)
In...
Will the available Volume of oxygen gas for use of patients increase when the pressure decreases from 12.4 MPa to 500 KPa?
Is using boyle's law the right way to calculate the available volume?
Really need to help getting started with this one.
They've given NPSH = (Ps - Pvp)/qg
Where Ps = Suction pressure at pump inlet
Pvp = vapour pressure of liquid at temp of pumping
q = density of liquid
g = acc due to grav
They've also provided Darcys friction Equation
The examiners tip (its a...
I've google all the keywords like "eductor", "ejector", "Venturi pump". All of them are the mechanism or applications that utilize "Venturi Effect". All of them are trying to explain the "suction effect" by saying that restriction area makes the fluid's velocity higher and hence lower pressure...
Part of me thinks this is could be a u-sub b/c x^3's derivative is 3x^2, a factor of 3 off from what e is raised to...but it is not a traditional u-sub...any thoughts if this is a u-sub or by parts, and what u should be?I know that there is more to solving the equation after this ( z =...
P1 = 5psi P2= 15psi , Z2-Z1 = 0, i assume V2 =V1 because velocity of water is the same everywhere in a pipe of constant diameter
is H friction = H pump = 10psi ?
Please help
So the Bernoulli's Equation..
My question : Are the terms on the left hand side equal to the total mechanical energy? So can I rewrite this equation as ?
Hello,
I think I understand how Bernoulli equations works but I am clearly uncertain on some aspects of its application. For example, let's look at the figure below:
1) The static pressure is ##60## ##psi## from the city water supply. There is not flow (tap closed) so the pressure at the...
In one pipeline with pressure P1 area A1 decrease to A2 we want to find P2 in area A2
we have bernoulli equation
p1+1/2 ρv^2=p2+1/2ρv^2
with low of conservation of mass A1V1=A2V2 that we can write V2=A1/A2 V1
if we keep in bernouli equation we have
P2=P1+1/2V2(1-(A1/A2)^2)
my quation is...
so far I have found the velocity 1 and 2 by dividing the volume flow rate over the area which I got from pi x dia squared/4 my v1 = 1.01859m/s and v2= 2.82942m/s i have then figured out a pressure for the 15mm pipe which i got an answer of 2.71 bar however i am stuck on the rest of the question...
Afternoon, anyone that would like to take a look at this Differential Equation problem it would be very helpful. I have tried separating the problem, but I am only working with one known term.
Consider the logistic equation
$$\dot{y}=y(1-y). $$
(a) Find the solution satisfying $y_1(0)=6$ and...
Consider a fixed horizontal tube of uniform cross section with pressure being 1atm at one of it's end and 5atm at the other (former due to 'open to atmosphere' and latter due to force on a piston), then liquid would flow towards low pressure end. By equation of continuity all cross sections will...
Homework Statement
We have a plane which lift area is A=500 m2 and weight of plane is m= 540 000 kg.
That the plane can stay in air the pressure difference between top and bottom of the lifts have to be:
B>G --> Δp= (m*g)/A = 10 594.8 Pa.
Homework Equations
Bernoulli equation
The Attempt at...
Homework Statement
What gauge pressure is required in the city mains for a stream from a fire hose connected to the city mains to reach a vertical building of height 15m?
Homework Equations
Bernoulli Equation
The Attempt at a Solution
I have tried this sum. My confusion is regarding choice of...
Hi
I have been reading some internet articles that state the Bernoulli equation does NOT explain the Magnus Effect. The articles state that the effect is due to circulation (Bernoulli requires inviscid flows)
Could someone explain the cause of the Magnus effect without reference Bernoulli's...
<< Mentor Note -- thread moved from the schoolwork forums to ME for better views >>
1. Homework Statement
Not really homework as this is for work. We are washing a cylindrical container (15.5 cm) with only one (1.8" dia) hole at the bottom the rest is sealed. Our machine sticks a .5" pipe with...
Homework Statement
A large water tank, open at the top, has a small hole in the bottom. When the water level is
## 30## ##m## above the bottom of the tank, the speed of the water leaking from the hole:
A. is ##2.5## ##m/s##
B. is ##24## ##m/s##
C. is ##44## ##m/s##
D. cannot be calculated...
Homework Statement
What gauge pressure is requried for water in a water supply line to reach a vertical height of 15m?
Homework Equations
Bernoulli Equation
The Attempt at a Solution
I have tried this numerical by taking velocity at ground level to be equal to velocity at top i.e. 15m height...
Hi,
I'm a little confused about the theory behind this problem related to fluids/Bernoulli's equation:
"An airplane wing is designed so that the speed of the air across the top of the wing is 251 m/s when the speed of the air below the wing is 225 m/s. The density of the air is 1.29 kg/m3...
Homework Statement
This was a problem on my fluids final and I'm trying to figure out if my rationale was correct here. The problem was an open air tank filled with water and at the bottom was a pipe pointing straight down. You had to find the exit velocity at the bottom of the pipe and account...
I have been involved in a fairly furious debate about a fluid dynamics experiment regarding the pressure of air passing through a tube attached to a moving car. It is similar in concept to the issue of whether or not an opening in an aeroplane fuselage would suck people out, where the opening...
I´m able to derive Bernoulli equation from the force bilance of the flowing element (particle):
dm\cdot \left (\frac{D \vec{v}}{D \tau } \right )_{flowing particle}=\vec{dF}_{g}+\vec{dF}_{p}
where dFg is the gravitational force acting on the particle, dFp is the pressure force acting on the...
Hi, I have never found a satisfactory explanation for why the Bernoulli equation is not valid when the streamline passes through a turbine, pump or another work transferring device. I have read many books that simply state this limitation without providing a convincing reason.
Bernoulli...
I 90% understand the question and solution but unfortunately I have some hesitations about the formal solution in the book.
First of all, when calculating P4-P3, choosing lines and points on them, why do book assume velocities of 3 and 4 to be the same...
Here is an illustration of something that came into my head:
http://imgur.com/a/V9V8S
(also attached to question)
If we do a energy balance (in terms of head) between point 1 and point 2 (ignoring friction for now, it's not really important):
$$\frac{P_1}{\rho g} + \frac{v^2_1}{2g} + z_1 +...
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...
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...
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...