What is Bernoulli's equation: Definition and 190 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.
Dear all,
I have found in the literature that if there is a open tank discharging water into the atmosphere the pressure at the discharge point is considered to be equal to the atmospheric pressure.
If one looks to the Bernoulli's equation and assuming no friction:
Pressure +...
Solve for v1
P1 + (1/2)ρv1^2 = P2 + (1/2)(v1r1^s/r2^2)^2
I am attempting to solve this equation for v1, but I am getting stuck on some algebra. How do I solve for v1? I can't figure out how to do it without eliminating v1 altogether because I have a v1^2 on both sides of the equation.
I am reading through my fluid mechanics book and there is a derivation of Torricelli's theorem i.e. V = \sqrt{2gh}.
The author's pick the datum line at the middle of the jet and show that:
h = \dfrac{p}{\gamma} + \dfrac{V^2}{2g}
where h is the distance from the jet to the surface of the...
It's just a simple question about the pressure under and over the plane's wing problem that I'm trying to answer. Well, actually I've already answered it, but one just keeps bugging me. Why don't we consider the difference in altitude of the lower and upper points of the fluid (air) when we use...
Homework Statement
This book is skipping over too many steps
where A1 = 1m2
A2 = .5 m2
y1 - y2 = 5m
The Attempt at a Solution
I'm having trouble getting from one step to another.
By my reckoning this equation
can be simplified by removing P0 and ρ since they are the same on both...
A Pitot-static tube connected to water manometer is used to measure the velocity of air. If the deflection between the two arms of the manometer is 12.4cm, determine the air velocity when the density of air is 1.25kgm-3 and the density of the water in the manometer is 1000kg/m3.
I am not...
Again-- I'm not entirely sure if this goes to physics or engineering, but the word thing that comes in mind when I hear Bernoulli equation is PHYSICS, so I decided to post it here...
Homework Statement
So I have this hydraulic system...
Homework Statement
Water is flowing from left to right through the system shown below. If the reading on
the pressure gauge is 384 kPa, what is the power input from the pump? Ignore energy
losses.
Homework Equations
Conservation of Mass (Q = vA)
Bernoulli's Equation (Total Head = Elevation...
Homework Statement
If wind blows at 35m/s over a house, what is the net force on the roof if its area is 240m^2 and is flat?
Homework Equations
P=F/A and P1 + 1/2pv^2 = constant
The Attempt at a Solution
I have no idea on how to find pressure, because if I sub it into P1 + 1/2pv^2 =...
Homework Statement
I need to find the net force acting on a flat squared roof with area A while the wind is blowing outside at some velocity, v_1.
Homework Equations
Bernoulli's Equation:
P_1+\frac{1}{2}\rho v_1^2+\rho gy_1= P_2+\frac{1}{2}\rho v_2^2+\rho gy_2
The Attempt at a...
Homework Statement
In bernoulli's equation derivation, we use Work energy theorem, in which work done is taken as change in kinetic energy plus change in potential energy.
But in mechanics, i have studied, Work energy theorem is simply change in kinetic energy.
So, which is correct? Pls...
I have a venturi tube and downstream of it, there is a small secondary opening at the end of the throat. This is where the local vacuum is created as the velocity increases and the pressure decreases. This difference between this pressure and the atmospheric pressure will induce air into the...
1. The density of the liquid flowing through the horizontal pipe in the drawing is 1200 kg/m3. The speed of the fluid at point A is 7.5 m/s while at point B it is 11 m/s. What is the difference in pressure, PB – PA, between points B and A?
2. Bernoulli's Equation P1 + 1/2 pv1^2 + pgy1 = P2 + 1/2...
Homework Statement
Skill Level II Problem
Use the Continuity equation to explain how jet engines provide a forward thrust for an airplane.
Skill Level Problem III
The Contintuity Equation is related to a powerful equation from fluid dynamics called Bernoulli's Equation. Do the research...
I'm not sure if this is the right place to post this (because it isn't homework), but it could easily be a homework question.
This wiki page, http://en.wikipedia.org/wiki/Siphon#Explanation_using_Bernoulli.27s_equation", shows how to apply Bernoulli's equation to a siphon where both the surface...
Blood flow...
Relating the Continuity of flow equation (A1v1 = A2v2) with Bernoulli's equation, with Poiseuille's equation.
Continuity of flow equation tells us this: when the area decreases, the velocity increases in order to maintain a constant flow rate.
Bernoulli's equation tells us...
Homework Statement
Here is the problem, I am able to calculate the velocity, but I don't know where to go from there.
A legendary Dutch boy saved Holland by plugging a hole in a dike with his finger, which is 1.10 cm in diameter.
(a) If the hole was 2.40 m below the surface of the North...
Homework Statement
The gauge pressure in a horizontal fire hose of diameter 5.4 cm is 3.0 x 105 Nm-2 and the speed of flow is 4.0 ms-1. The fire hose ends in a metal tip of diameter 2.5 cm. What are the pressure and the speed of the water in the tip?
Homework Equations...
Homework Statement
Consider a water pipe that tapers down from a diameter d_A = 5.0 cm at end A to a diameter d_B = 2.5 cm at end B. At each end a vertical pipe that is open to the air at the top is attached to the pipe. Assume that water flows through the pipe at high enough pressure that the...
Homework Statement
Conceptual question. I have a cylindrical container with a hole at the bottom and a water level filled to just before a sloping neck towards the top (area at the top of the neck is smaller than before it slopes). How would the velocity of the water leaking through the bottom...
Homework Statement
A perfectly spherical golf ball with a specific gravity of 0.55 is dropped from a height of 10 m above the surface of a smooth lake. Determine the maximum depth to which the ball will sink. Neglect any frictional loses or energy transferred to the water during impact and...
Homework Statement
Figure 1.1. shows a simplified diagram of the camping stove used by a famous scientist up a mountain, in which gas under pressure is transported to the four nozzles via metal piping. A valve is used to control the flowrate by reducing the delivery pressure to a maximum...
Homework Statement
Consider a spherical bubble of radius R,rising in water. Using Bernoulli's equation show that the rate of rise of the bubble is:
U=(2/3) \sqrt(gR)
Homework Equations
Bernoulli Equation
Potential Flow
The Attempt at a Solution
I have considered the...
ap physics student, on this for the first time
The flow rate of water through a garden hose is 60 cm3/s, and the hose and nozzle have cross sectional areas of 5.1 cm2 and 1.6 cm2 respectively.
(a) If the nozzle is held 11 cm above the spigot, what are the flow speeds through the spigot...
Homework Statement
You have a tank that is on top of a 1 meter post. The tank is filled with water to an unknown height. At the bottom of the tank there is a 3.5mm hole that is squirting out water a horizontal distance of .6 meters.
Homework Equations
Bernoulli's equation p1...
Hello,
I am having some difficulty in understanding the terms in Bernoulli's equation.
Bernoulli's equation is given as follows:
P + 0.5(rho)(V^2) + (rho)gh = constant (along a streamline)
The first term (P) is the Static Pressure.
The second term (0.5(rho)(V^2)) is the Dynamic...
Homework Statement
The water supply of a building is fed through a main pipe 6.00cm in diameter. A 2.00cm diameter tap is located 2.00m above the main pipe. When the tap is turned on it fills a 25.0L container in 30.0s if no other taps are turned on at the same time.
a) What is the speed at...
Homework Statement
A very simplified schematic of the rain drainage system for a home is shown. Rain falling on the slanted roof runs off into gutter around the roof edge it then drains through downspouts into a main drainage pipe M below the basement which carries the water to an even larger...
1. Homework Statement
A static electrically conducting fluid, in the presence of electric and magnetic fields, experiences a Lorentz force. Determine the fluid pressure at point (1,2,1) when the pressure LaTeX Code: p_{0} at origin (0,0,0) is under the effect of gravity and the electric and...
I'm no good with fluid dynamics. I really am willing to improve can someone point me to what equation I should use for this question. I assume its bernoullis equation? I've drawn a diagram of how I see the pipe.
To make things worse I haven't done fluids in quite a while.
Homework...
Homework Statement
A static electrically conducting fluid, in the presence of electric and magnetic fields, experiences a Lorentz force. Determine the fluid pressure at point (1,2,1) when the pressure p_{0} at origin (0,0,0) is under the effect of gravity and the electric and magnetic field...
[SOLVED] Bernoulli's equation & U-Tube
Homework Statement
Air flows through this tube at a rate of 1200 cm^3/s . Assume that air is an ideal fluid.
What is the height of mercury in the right side of the U-tube?
Homework Equations
Bernoulli's Equation (P1 + 1/2*rho*V1^2 +...
Hi guys, we use bernoulli's equation for inviscid flows, like water and gas.
But for gases, we also have the ideal gas law, let's say if i want to calculate energy within a gasous system, like a gas in a fixed space (e.g. a room; a tank etc...)
Looking at ideal gas law, PV=mRT, PV will give...
Water flows through a 0.30m radius pipe at the rate of 0.20m^2/s. The pressure in the pipe is atmospheric. The pipe slants downhill and feeds into a second pipe with a radius of 0.15m, positioned 0.60m lower. What is the gauge pressure in the second pipe?
So, what I've figured from the...
Before I describe the problem, I would like to apologize for my lack of comprehension
of this subject. It is the first semester of Physics, but the end, and has become quite
complicated.
Homework Statement
There is a 2.0 L soda bottle used, with a hole a certain height (hhole) from
the...
A fountain shoots a vertical jet of water at a rate of 0.33 L/s to a height of 1.6m.
What is the initial speed of the jet and what is the radius of the hole out of which the jet passes?
What pressure must the pump of the fountain supply? (Assuming that it sits just below the emerging jet).
At...
Homework Statement
A cylindrical bucket of liquid (density ρ) is rotated about its symmetry axis, which is vertical. If the angular velocity is ω, show that the pressure at a distance r from the rotation axis is
P = P_0 + \frac{1}{2} \rho \omega^2 r^2
where P0 is the pressure at r = 0...
Homework Statement
Water flows at 0.61 m/s through a 3.0 cm diameter hose that terminates in a 0.30 cm diameter nozzle. Assume laminar non-viscous steady-state flow.
(a) At what speed does the water pass through the nozzle? (Correctly solved to be 61 m/s).
(b) If the pump at one end of...
Homework Statement
An incompressible fluid is flowing through a vertical pipe with a constriction. The wide section is 2.00 cm in diameter and is at the top of the pipe. The pressure of the fluid in the wide section at the top is 200 kPa. The velocity of the fluid in the wide section is 4.00...
Homework Statement
What is the lift (in Newtons) due to Bernoulli's principle on a wing of area...m^2 if the air passes over the top and bottom surfaces at speeds of ...m/sand ...m/s, respectively? I've given the values but I just want to know if I'm doing the problem right conceptually...
A fire hose must be able to shoot water to the top of a building 35.0 m tall when aimed straight up. Water enters this hose at a steady rate of 0.500 m3/s and shoots out of a round nozzle.
i) What is the maximum diameter this nozzle can have?
ii) If the only nozzle available has a diameter...
Homework Statement
Using the data of Example 10-11, calculate the average speed of blood flow in the major arteries of the body, which have a total cross-sectional area of about 2.0cm2
Homework Equations
well... Actually, I don't know how to solve this problem.
The Example 10-11...
Homework Statement
The figure below shows a stream of water in a steady flow from a kitchen faucet. At the faucet the diameter of the stream is 1.20 cm. The stream fills a 125 cm3 container in 18.2 s. Find the diameter of the stream 13.0 cm below the opening of the faucet. (The answer should...
My mind is struggling trying to understand how a decrease in pressure can increase the velocity and vise versa for a fluid that is flowing through a tube of some kind. I've always thought that if you increase the amount of pressure then the velocity should also increase. It appears that they...
Hey,
Here's something that confuses me with the Hagen–Poiseuille equation and the Bernoulli's equation. From the Hagen–Poiseuille equation and in general, fluid will tend to flow from high to low pressure. From Bernoulli's equation pressure is a function of cross-sectional area and...
Homework Statement
An open can is completely filled with water, to a depth of 20.6 cm. A hole is punched in the can at a height of 1.7 cm from the bottom of the can. Bernoulli's equation can be used to derive the following formula for the speed of the water flowing from the hole.
In...
Hi,
Hopefully a very simple question for someone that knows; We know from Bernoulli's principle that an area of high velocity creates an area of low pressure and vice versa. My question is how is this created?
Thanks
Homework Statement
A venturi meter is a device for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at a speed v2 through a horizontal section of pipe whose cross-sectional area A2 = 0.0600 m2. The gas has a density of ρ = 1.60 kg/m3. The Venturi meter has a...