Bernoulli equation Definition and 133 Threads

Question From Paper: A hot air balloon has an envelope which has height h = 30 m high (see below). The balloon is always operated with a temperature difference between the heated gas and the atmosphere of 100K. For simplicity, assume that the envelope contains heated air only (that is, ignore...

Hello everyone, I’m working on a project where I need to use a cylindrical tube with a vacuum pump to suck in mechanical parts. The tube approaches the part, and the vacuum generated by the pump draws the part into the tube. I want to understand how to link the key parameters of the system: the...

If this formula were to be correct, if we use the liquids in the Venturimeter and the tube to be of the same density, the velocity would come out to be zero which makes no sense. I calculated the formula and got a slightly different numerator. Am I correct?

TL;DR Summary: We know that the fluid pressure at the exit of the pipe is Patm but what about before the exit? How can we calculate that pressure using Bernoulli's equation. Hello everyone☺️. Please help, i'm seriously stuck 🫠🙇‍♀️ When learning about bernoulli's equation there's a classic...

The problem: Its solution: I am sure that the velocity ##v## can be calculated by using Bernoulli's equation, but I fail to calculate it. I don't know what pressure is at the hole - is it ##h_2 \rho g## or ##(h_2 - h_1) \rho g##? The pressure of the water "under" the hole is ##h_2 \rho g##...

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...

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...

Would it be because I'm comparing two different streams as opposed to two portions of the same stream?

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...