Bernoulli equation Definition and 133 Threads

First, this is is not a homework problem, per se, but it is a conceptual difficulty I am having with my physics 1 course, in which we are studying fluid mechanics (moderators please move this post if there is a more appropriate subforum). Homework Statement I was going over the derivation...

Homework Statement Liquid, specific density 0.8, flows with velocity 4 m/s in a pipe that has a downward slope of 1:50. At a certain point in the pipe, a pressure gauge shows a pressure of 80 kPa. Determine the pressure at a point 200 m downstream of the gauge if: flow losses are ignored...

In the Bernoulli equation, i know that velocity is in m/s and mass in N which gives energy in joules. Likewise potential energy id also in joules being mgh. In pressure energy what are the variants? i.e what is formula for calcualting the pressure energy term in the equation? If we compute...

Hi all, I've got a nonlinear differential equation of the general form y' + f(x)y + g(x) = h(x)(y^n) to solve. For g(x) = 0 this is your standard Bernoulli equation. I've been trying to think of a way to solve it but haven't managed so far. Any ideas would be appreciated. Many...

I'm practicing first-order linear differential equations, and have come across something I find interesting - being able to reduce nonlinear equations to linear equation with appropriate substitutions. I'll start with the well-known Bernoulli equation, and if there are other ways to do this...

Homework Statement How can I rearrange this equation to graphically show that hole diametre is inversely proportional to sink time? So my experiment results show a nice diametre=1/t , and I would now like to take the equation I've come up with to show this relationship within the equation...

Homework Statement The hydrostatic pressure term in the Bernoulli equation (ρgz) decreases with fluid depth. Why? Homework Equations Bernoulli Equation (multiplied by density ρ to give us pressure units): P+\rho\frac{V^2}{2}+\rho gz=constant The Attempt at a Solution In the hydrostatics...

Homework Statement My book says that each term in the Bernoulli equation (when divided by ρ, has pressure units). I don't see how. Homework Equations The Bernoulli equation for steady, incompressible flow is: \frac{P}{\rho}+\frac{V^{2}}{2}+gz=constant The Attempt at a Solution...

I'm trying to ascertain the dynamics of a compressed air system in terms of flow rate, air consumption, pressure drop etc. To keep it simple my system consists of a 5.5 bar supply (550000Pa) supply on 12mm OD Nylon Tubing and is reduced to 6mm OD Nylon through a valve (pressure drop assumed...

I've been unable to fully solve this: \frac{dy}{dx} + y = xy^4 The U: u = y^{-3}, so y = u^\frac{-1}{3}, and \frac{dy}{dx} = \frac{-1}{3}u^\frac{-4}{3}\frac{du}{dx} The substitution: \frac{-1}{3}u^\frac{-4}{3}\frac{du}{dx} + u^\frac{-1}{3} = xu^\frac{-4}{3} Simplified: \frac{du}{dx} -...

Homework Statement Flow rate in Venturi meter of Petrol (SG 0.85). Diam1 - 0.2m Diam2 - 0.15m Height Diff in manometer of Mercury (SG 13.6) 0.012m, so Δp= 13600 x 9.81 x 0.012 = 1601? Cd = 0.98 Homework Equations Bernoulli, p/ρg + U2/2g + Z U=Q/A The Attempt at a...

dear PF.. what is the Bernoulli equation in terms of energy per unit volume the equation include the 1) static pressure 2) hydrostatic pressure 3) dynamic pressure 4) stagnation pressure

ODE, bernoulli equation --> leads to crazy integral ! Homework Statement An Initial Value Problem, ODE (Bernoulli equation) ODE: [x^2]*y' + 2*[x^3]*y = [y^2]*(1+2*[x^2]) IV: y(1) = 1/2 Homework Equations general form of Bernoulli's equation: y' + a(x)y = b(x)*[y^n] First...

Hi! I came across a problem involving a spigot. In order to find the velocity in the spigot which is located h meters in the tank, one uses the reduced V= sqrt (2gh) equation... how is this different from using V1A1 = V2A2? When would you use this equation? For instance, say you have a...

Homework Statement solve the differential equation y'(t)=-4y+6y^3 Homework Equations The Attempt at a Solution I'm pretty sure (not positive) that this is a Bernoulli Equation. I've been following this wiki in an attempt to solve...

Homework Statement y'+3y=e^(-3x)*y^4 , IC: y(1) = (12/4e^-3)^(-1/3) Homework Equations Bernoulli Method The Attempt at a Solution So n=4, i can substitue u=y^-3 u'+(-3)(3)u=(-3)e^(-3x) determine an integrating factor of e^-9x, then integrate both sides...

Homework Statement water flows steadily with negligible viscious effects through this pipe. the 4-inch diameter section of the thin walled tubing will collapse if the pressure within is at 6 psi below atmospheric pressure. determine maximum h so that the tube won't collapse. final...

I have solved the following Bernoulli equation by letting Z = y1 - 2: xy' - 2y = x3y2. I obtained the solution y = 5/(5c1 - x5) which Wolfram Alpha has confirmed. From this result, I have obtained y' to be y' = 25x4/(5c1 - x5)2 The problem is when I go to check the solution by plugging...

An object is accidentally dropped into a water pipe. Pressure applied to pipe is 10 atm. The depth of lake is 10m. What will be speed of object when it exits the pipe and first enters the lake? Assume that the object is carried along with the surrounding water and does not affect flow of...

Homework Statement Homework Equations X=Vo*tfall Bernoulli Eq: \frac {p}{\rho}+\frac{V^2}{2}+gz=const I used B.E. to find an expression for the velocity of the exit jet: V_o=\sqrt{2g(H-h)} For some reason I am confused as to how to find an expression for t_fall ? I know it should be...

Hi, urgent question. Bernoulli's equation seems to be conservation of energy. I read that it's only for incompressible flows; but isn't the term involving pressure the energy due to the work done on a mass of air in compressing it? Thanks

well,i ve some problems with bernouuli equation.first,i'd like to ask abt meaning of static pressure in flowing fluid because i really ve read abt that in references and many websites but still can't get exactly what's meaningt of static pressure in flowing fluid. i ve read on website that...

Hello friends, I have a problem in Bernoulli equation and Newton Law. I'm going to calculate how much power is needed to lift up an object with weight W. I'm planning to put the object in a 10 inches diameter. How can I calculate the power needed by the motor to lift up the object? Does...

Hi, I have some questions about this equation. P + (1/2)mv^2 + mgh = constant. So obviously (1/2)mv^2 is the kinetic energy, and pgh is the potential energy. 1.) Is this equation basically a statement of conservation of energy? 2.) If yes, then how exactly is pressure, 'energy'? I...

The Bernoulli Equation for non-uniform flows have a constant at the kinetic energy term which describes the velocity profile at that place. The problem is this, If a have water flowing through a pipe with a parabolic velocity profile and then the water exit the pipe at free jet and there is now...

How do I solve a Bernoulli equation of the form x' = b(t)x + c(t)x^n when n < 0?

Water is fed via a 200m long, 125mm diameter pipe to a field. The take is 12m elevation. the friction factor is 0.008 and k factors add up to 3.3. Pressure is all atmospheric and V1 is 0. Homework Equations Bernoulli Equation with the addition of friction, elevation and k factors...

Homework Statement I have a pump pumping 50 gallons per minute of water from a tank at atmospheric pressure to another tank at atmospheric pressure. The main discharge pipe (internal diameter is 4.03 inches) is divided onto 5 smaller pipes (internal diameter is 1.05 inches). The pressure on...

Homework Statement x^2y' + 2xy = 5y^3 Homework Equations Bernoulli Equation The Attempt at a Solution so... v=y^-2, y=v^(-1/2) y' = -1/2v'v^(-3/2) moving everything over... y'/y^3 + 2/(xy^2) = 5/x^2 and plugging everything in... -1/2v' + 2v/x = 5/x^2 v' - 4v/x = -10/x^2 v' -...

it...just...does...not...make...the...slightest...sense...to...me...:confused: Here it goes... y' + \frac{y}{x} = 3x^2y^2 This is a Bernoulli equation with P = \frac{1}{2}, Q = 3x^2, and n = 2. We first divide through by y^2, obtaining... \frac{1}{y^2} \frac{dy}{dx} + \frac{y^-^1}{x} =...

can someone explain how to solve the bernoulli equation? I'm having a hard time understanding...

I cannot get the correct answer to this for some reason: t^2y'+2ty-y^3=0 I use the substitution v=y^{1-n}=y^{-2}\implies y=v^{-\frac{1}{2}} and come up with y'=-\frac{1}{2}v^{-\frac{3}{2}} and y^3=v^{-\frac{3}{2}}. -\frac{1}{2}t^2v^{-\frac{3}{2}}+2tv^{-\frac{1}{2}}-v^{-\frac{3}{2}}=0...

Was wondering if it was possible to derive the best possible shape of a boat hull to achieve maximum speed? As it is the equation on how to calculate the speed of a sphere moving in water... or else I am just totally wrong and you can bluntly ignore this post :-p