Bernoulli Definition and 329 Threads

\frac{dy}{dx} - \frac{1}{x}*y + \frac{1}{y^2}*x = 0 This is a bernoulli differential equation which follows the following procedure http://en.wikipedia.org/wiki/Bernoulli_differential_equation Can someone provide the full steps because somewhere I am mistaken?

Hello everyone, Thank you to all who offer their help. Homework Statement If the volumetric output of the pump were increased, keeping the pipe diameter constant, would the pressures at A, B, and C increase or decrease? Would the heights within each column at each location rise or fall...

Confidence intervals [b]1. Homework Statement [/ Use CLT to construct approximate symmetric 100(1-alpha)% confidence interval [L,R] for p then show that [L,1] is then an approximate 100(1-alpha/2)% confidence interval for p The Attempt at a Solution When [L,1] then we have a one...

Homework Statement Show how Var(Xi) depends on p writing it as a function \sigma^2(p) The Attempt at a Solution Var[Xi] = E[Xi^2] - E^2[Xi] = p-p^2 = p(1-p) not sure where to go from here to get it in the form \sigma^2(p) ?

Refering to the image uploaded can we say by applying bernouli equation and darcy equation the following : Pa/(guamma) + Va^2/2.g + Za - (head loss in pipe ab using darcy equation )-(head lossin pipe bc using darcy equation) = Pc/(guamma) + Vc^2/2.g + zc . ?? and the same thing between...

Homework Statement Suppose we want to estimate a binomial proportion, p. We take a sample of size n and count X successes. Consider a Bernoulli random variable, Y that is 1 with probability p and 0 otherwise. Show that the mean and variance of Y are p and p(1-p), respectively...

Suppose you have multiple independent Bernoulli random variables, X_1,X_2,...,X_n, with respective probabilities of success p_1,p_2,...,p_n. So E(X_i)=p_i, and E(X_i+X_j)=E(X_i)+E(X_j). Also, \text{var}(X_i)=p\cdot (1-p), and \text{var}(X_i+X_j)=\text{var}(X_i)+\text{var}(X_j). (Though...

I keep getting stuck on one part of the equation. can somebody help? dy/dx = y(xy3 - 1) dy/dx = xy4 - y dy/dx + y = xy4 u = y1-n = y-3 y = u-3 dy/dx = dy/du * du/dx dy/dx = -3u-4 du/dx Substituting terms into the original equation -3u-4 du/dx + u-3 = x(u-3)4 Here is where I get stuck...

Let X be the set X=\left\{x_1,x_2,...,x_n\right\}, where each x_i is a Bernoulli random variable and P be the set P=\left\{p_1,p_2,...,p_n\right\}, where p_i is the probability that x_i=1. Now, suppose there are two other sets, A=\left\{a_1,a_2,...,a_n\right\} and...

Ok I studied bernoulli and I can see how fluid would travel faster in narrowed regions but in most examples I see when something is narrowed the flow is reduced. Is this because of resistance? Also when there is resistance speed in the narrowed section is reduced right? I like to know what do...

I know the topic has been dealt in the past, I read it but still couldn't extrapolate a satisfying answer. I would like to know how Berboulli equation applies to a hose without restrictions in which fluid (water) exits at atmospheric pressure, the typical garden situation without any nozzle. I...

Ok after hours of contemplating I think I finally understood the concept(hopefully ). However I still need 1 quick clarification. When water flows suddenly from a larger to a small dimater Bernoulli says 1. Pressure decreases 2. Velocity of fluid increases I'll put numbers just for...

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...

sorry for the "bad" title, I couldn't think of anything else. We all have seen the experiment where you take a hair dryer and a ping-pong ball and the hair dryer blows the ball into the air and you can move and tilt the ball around... now, that is a very simplified version of my final...

Homework Statement I recently was given an interesting problem I thought I'd share with the community here. It's a fun exercise in mathematics. Given the equation: Po/P = [1+((k-1)/2)*Ma^2]^(k/(k-1)) From this stagnation ratio, derive the Bernoulli Equation: Po = P + 1/2 * rho * V^2...

say you perform one bernoulli experiment where outcome X = 0 and X=1 are failure and success, respectively. then you have P(X=0) = 1-p and P(X=1) = p. what if you expand this to two bernoulli experiments? only 1/4 cases would be successful, so you would have: P(X=1) = p^2 E(X) = p^2...

I am trying to follow along with the text's derivation of the Bernoulli equation and I am a little confused with a particular line. The images show an elemental streamtube control volume (CV) of variable area A(s) and length ds. We assume that though the properties may change with time and...

Is this a known bernoulli number conjeture/theorem?: The denominators of B_n (when expressed as an irreducible fraction), doesn't contain as a factor powers of prime numbers (ex. isn't divided by 5^2) Example: B_2 = 1/6 6 = 2*3 B_4 = -1/30 30 = 2*3*5 B_{24} = -236364091/2730 2730...

Homework Statement 3y^2*y'+y^3= e^-x The Attempt at a Solution I am using Bernoulli's equation to substitute V in and I keep coming out with Y^3= e^x(-e^-x+c) my V = y^3 Y = v^(1/3) and dy/dv=(1/3)v^(-2/3) I peeked to see if I was correct, the right answer is supposed to...

Ugh Bernoulli Equations! Homework Statement dy/dx = y(xy^3-1) I tried to set it up and use the bernoulli equation method as a substitution but it didn't work. Any tips? The Attempt at a Solution I set u=y^(-3) and had it set up like this dy/dx + y = xy^4 Ok HELP...

http://up2.up-images.com/up//uploads2/images/hosting-036ee42f15.jpg in the figure, which ball will win in the race? note: there is no energy loss

1. The problem statement. 1. http://img194.imageshack.us/img194/3815/linear.png 2. http://img25.imageshack.us/img25/1543/bernoulli1.jpg 3. http://img23.imageshack.us/img23/7991/bernoulli2.jpg 2.Relevant equations Problem 1 is Linear Differential Equation and Problems 2 and 3...

Is nothing of the Bernoulli effect due to friction? Passing fluid trying to lift away a slower interface?

Problem:y' + y(1/x) = 3 x^2 y^2 Solution:p(x)= 1/x q(x) = 3x^2 <--- These are countinuous functions on the interval (0,+inf) y^-2[y' + y(1/x) = 3 x^2 y^2] A => y'y^-2 + y^-1(1/x) = 3x^2 v = y^(-n+1) = y^-1 v' = -y^-2 y' Plugin to problem A v' + v/x = 3x^2 B p(x) = 1/x...

Hello there! It's been about a grillion degrees up here in my home town recently and last night this led me to a sort of conundrum. If I open the window in my room but leave my door shut, hardly any air comes it at all. If I open my door, there's a strong puff of wind that comes into the room...

I have a bet with one of my friends, it has to do with the bernoulli equation that says the higher the velocity of a gas, the lower the pressure. I came up with an invention idea that involves a gas cylinder, the gas cylinder has a maximum pressure of 4000 PSI and the gas inside exerts...

"Mathematics holds a vital place in a wide variety of fields, including the sciences and finance. Number calculations have proved the viability of countless scientific phenomenon. Money lenders generally need statistical data to evaluate a consumer’s financial situation before granting them a...

Homework Statement Homework Equations Bernoulli eq and Conservation of Mass The Attempt at a Solution Treating the ENTIRE system as my control volume, from conservation of mass we have: \frac{d}{dt}\int\int\int_{cv}\rho\, dV +\dot{m_2}-\dot{m_1}=0 \Rightarrow \frac{d}{dt}\int_h\rho A_o\...

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...

Hello I’ d like to have your thoughts about any temperature variation when a fluid passes through a narrower part of a tube, a subject quite rarely discussed.. Can we start with « perfect Bernoulli conditions »and an incompressible fluid having only translational energy,. flowing theough a...

Homework Statement Find the general solution of the following differential equation. y'+4xy=10xy2cos(x2) Homework Equations The usual Bernoulli equation ones: y'+p(x)y = g(x)ya u(x)=[y(x)]1-a u'+(1-a)pu = (1-a)g The Attempt at a Solution I got up until the general solution part.. I'll just...

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

Hey everyone, I need some help trying to figure out how to find the summation of n \sum_{}^{\6}i^p i=0 I was looking on the web and found on Wikipedia this formula off the http://en.wikipedia.org/wiki/Summation" page. It looks like this assuming I copied it right (ignore the periods)...

Homework Statement Solve the Bernoulli equation, y'(x) - 4y(x) = 2e^(x) * sqrt(y(x)) Homework Equations y' + P(x)y = Q(x)y^n - Bernoulli Eqn e^(∫P(x) dx) - Integrating Factor The Attempt at a Solution y' - 4y = 2e^(x) * y^(1/2) Divided both sides by y^(1/2) y'/y^(1/2) - 4y/y^(1/2) =...

Is Bernoulli principle the cause of suction truck?? Hello! I’d like to know this question: When a truck walks to a high speed we see how the road tree leaves are dragged behind it. I would like to know the real cause of this problem. I think the air viscosity makes the truck drag a thin...

Homework Statement The Bloch-Gruneissen approximation for the resistance on a monovalent metal is \rho=C(T^{5}/\Theta^{6})\int^{\Theta/T}_{0}\frac{x^{5}dx}{(e^{x}-1)(1-e^{-x})} (a)For T->\infty, show that \rho=(C/4)(T/\Theta^{2}) (b)For T->0, show that...

Hi, I am stuck on this question as I haven't encountered anything similar to it. Normally I have only dealt with pipe with one inlet/outlet. Homework Statement I am given a diagram of the pipe shown on the attachment (Sorry for the crude diagram). Hosted it while the attachment is "reviewed"...

Hello ppl. I have a problem in finding out the volume of solid formed by the revolution of one loop of lemniscate of bernoulli ( r²=a²cos2θ) about the initial line θ =0 Using the relevant forumula for the volume of the solid generated by the revolution of one loop of the polar curve about the...

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...

For a stationary disk, the air pressure on the platter is atmospheric pressure. For a disk spinning at 10,000 RPM, say 140 miles per hour for a 5.25 inch disk, I assume the Bernoulli effect would reduce the pressure, but because of the Ekman flow, the pressure would be more than the pressure...

Homework Statement Find the lift in Newtons due to the Bernoulli Principle on a wing of a plane of area 84.5 m^2 if the air passes over the top and the bottom surfaces at speeds of 347m/s and 289 m/s Homework Equations P1+(1/2)densityV^2 =P2+(1/2)densityV^2 The Attempt at a...

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?

Help with first order, "Bernoulli" ODE We just covered: -First order linear ordinary differential equations -Bernoulli Equations -Simple substitutions. This problem was assigned. Its supposedly a Bernoulli equation with respect to y, but I can't figure it out...

[SOLVED] River channel problem using Bernoulli and Continuity Homework Statement A river (100 m wide) flows through its rectangular channel at a depth of 2.560 m at a velocity of 2.050 m/s. What is the velocity of the discharge if the channel is narrowed to 90 m? Homework Equations...

Homework Statement A long horizontal hose of diameter 3.8 cm is connected to a faucet. At the other end, there is a nozzle of diameter 1.8 cm. Water squirts from the nozzle at velocity 38 m/sec. Assume that the water has no viscosity or other form of energy dissipation. a) What is the...

I don't know if this is appropriate or not, here or anywhere. However, I propose this thread be used to post recursive formula for the Bernoulli numbers. It saves a great deal of frustration. The first is simply, \sum_{k = 0}^{n-1} \binom{n}{k} B_{k} = 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...