Bernoulli's Definition and 306 Threads

Homework Statement xy(dx)=(y2+x)dyHomework Equations integrating factor : u(x)=e∫p(x)dx standard form of linear DE: dy/dx + P(x)y=Q(x) standard form of bernoulli's differential equation: dy/dx + P(x)y=Q(x)yn change of variables v=y1-n The Attempt at a Solution xy(dy)=(y2+x)dx xy(dy/dx)=y2 +x...

Homework Statement Use Bernoulli’s equation to calculate how fast the water emerges from the open tap (at position 2) in the figure(a). You may assume that the water at position 1 moves negligibly slowly (b) The tap is rotated to create a fountain as shown in (b) Calculate the maximum height h...

Homework Statement Homework EquationsThe Attempt at a Solution First I would like to mention that I have solved this problem using force approach and got correct result . My problem is that when I saw the official solution , I was quite surprised to see the application of Bernoulli's...

Hello, PF! I'm currently brushing up my fluid mechanics and came across some questions while studying the compressible flow of an ideal gas using Bernoulli's equation. First, consider incompressible flow in the following system Neglecting any changes in elevation, the Bernoulli equation for...

Seeing as P(F/A) + KE + PE = Constant, if the fluid's flowing through a constriction (So the area's decreasing(Which would net an overall larger pressure)), How does the pressure term decrease? Does the Force decrease even more greatly than the Area, to net an overall lower pressure? Assuming...

Homework Statement " A horizontal water pipe has a radius of 10 cm and a pressure of 8*10^4 Pa at one end. At the other end the radius is 5 cm and the pressure is 6*10^4 Pa. What is the water flow rate through this pipe? Homework Equations P1 + 0.5 * ρ * v1^2 + h1ρg = P2 + 0.5 * ρ * v2^2 +...

You and a friend of yours went for a drink of chocolate milkshake(ρ=1200 kg/m3). The waiter brings your drink in two glasses 200 mm tall with a straw 8 mm in diameter and 300 mm long. Given that human lungs capacity can develop approximately 3000 Pa of vacuum pressure and assuming that the straw...

Homework Statement This is a lab that we have to design and carry out that goes above and beyond our course. I am investigating how the diameter of a hole in a bowl affects its sink time when put in a larger bowl of water (saxon bowl, or sinking bowl as they are known.) I will have to plot them...

Homework Statement You have been given a milkshake (ρ = 1200kg/m^3). The glass is 200mm tall a straw 8mm diameter and 300mm long. Show that human lungs would be unable to drink the milkshake through a vertical straw. (answer should be around 3000Pa) I have no idea what to do as I don't know...

Hello! I have encountered some trouble with choosing the right reference points when using Bernoulli's equation and I would be glad if you could help me sort it out with this made up example. :) 1. Homework Statement There is a large, open, cylindrical water tank with a cross section area of...

Suppose there are two tanks, tank A and tank B, of equal size and both are very large. Suppose the bottom of tank A is at an elevation that is higher than the top of tank B. Suppose there is a very small tube relative to the size of the tanks that connects the bottom of tank A to the bottom of...

Hi all, I'm considering an fluids example that's giving me an apparent contradiction when I consider it from the perspective of Bernoulli's Equation vs. the Equation of Continuity. What I'm thinking of is the common observation that putting one's thumb over a garden hose results in an increase...

Homework Statement Water at 20°C flows through a capillary tube with an inside radius of 0.17 mm and a length of 5.9 cm. If the volume flow rate through the capillary is 1.9 cm3/s, what is the pressure difference between the two ends of the capillary? Give your answer in kPa. The viscosity of...

Hi i need a examples of beginning of bernoulli, i will do a presentation of this, i need a original example (object, which have to be a utility in our lives) of Bernoulli, my classmates, they already have a other examples like, aircraft, sailing, atomizer. So i need other one, easy to explain...

I hope this question doesn't have too obvious of an answer. Basically, I still cannot grasp why Bernoulli's equation applies for wind tunnels and pitot-static probes. According to my textbook ("Introduction to Flight" by Anderson), Bernoulli's equation holds only when comparing two points...

Hi Can anyone advise how the following equation was derived. http://uploadpie.com/PYLrD

(This is more of a conceptual question than a real homework question; thank you all so much for your help though!) :D 1. Homework Statement Let's say that I have a large soda bottle. I drill a small hole through the side of it, put my finger over it to seal the hole, and fill the bottle up...

Homework Statement An incompressible heated gas of constant temperature and pressure flows along an infinitely long tube at an unspecified velocity v1; a pressure of P1; and a density of p1 into an unheated open area of infinite volume containing the same gas at a lower pressure of P2; a...

1. The problem statement, all variables and given/know Say I have a can of water, and I am rotating it about its central axis at a constant angular rate. The water in the tank should make a 3D almost parabolic curve as it touches the the walls of the tank. Can I use Bernoulli's equation along...

Not a physics student -- but was thinking about how the A/C system works in a vehicle. First surprise was that pressure drops when a tube narrows. Seemed counter-intuitive as I was picturing taking a balloon and squeezing it -- would the pressure in the middle be lower than the ends? Then again...

The name of lectures of integral calculus written by Johann or Jeans Bernoulli (he is called by both names as far as I know) might be " lecciones mathematicæ de calculo integral". I searched for one day for the english translation, I couldn't even find the english title of his book on integral...

Hi everyone and thank you in advance. My first problem is: if v1=constan in a section S1, it should not be ∑ F = 0 ? Or maybe Σ M = 0 ? Because all forces that i recognize are gravity and pressure, but i never found the equation mg - PS = 0 or something similar. I was thinking about something...

Hi, I'm trying to understand vortex shedding and how the Karman vortex street occurs when air flows around a cylindrical object, so far it's going OK but then I came across this part of the explanation which leaves me confused: "Looking at the figure above, the formation of the separation...

Some days ago I got confused trying to solve an exercise about fluid dynamics. Trying to simplify the problem here is a similar situation: I have a cistern connected to a tube containing a fluid as shown in the picture below. Assumming that the fluid is incompressible... I know from the law...

Homework Statement Calculate pressure outside the box- ATM pressure is 101325 Pa, air moving outside the box is 45 m/s, air density is 1.3 kg/m^3 Homework Equations P + 1/2(roe)(v)^2 = Patm The Attempt at a Solution P + 1/2 (1.3kg/m^3)(45m/s)^2 = 101325 Pa P + 1316.25 Pa = 101325 Pa P=...

Homework Statement A water storage tank is open to air on the top and has a height of 1 m. If the tank is completely full and a hole is made at the center of the wall of the tank, how fast will water exit the tank? Homework Equations Pressure is the same as atmospheric pressure because the...

hello! I think Bernoulli's equation it's just an equation of conservation of energy. Am I right? but I don't understand how to apply the conservation of energy principle exactly. can you help me please? I get it that if the fluid moves, it has kinetic energy which is 1/2mV^2. I also get...

Homework Statement A closed and elevated vertical cylindrical tank with diameter 2m contains water to a depth of 0.8m. A circular hole is made at the bottom of the tank with diameter 0.2m.As the water drains from the tank, compressed air above the water in the tank maintains a gauge pressure...

Hey all, So I have a small convergent nozzle that I'm modelling in Abaqus and I'm wondering how I could work out the pressure distribution so I can apply the correct load. The problem is I only know the pressure being fed to it by air compressor. Is there a way to use Bernoulli s or some other...

for a stream line flow of ideal liquid (non-viscous) imcompressible the sum of pressure energy per unit volume kinetic energy per unit volume , potential energy per unit volume remains constant mathematically P+1/2roV2+ROGH=constant consider a fluid flowing in a pipe of various crossections we...

My understanding and application: Flowing blood with mass m, and velocity v has KE proportional to mean velocity squared as blood flows inside the vasculature, pressure is also exerted laterally against the walls of the vessels So, it is then reasonable to use Bernoulli's for the blood and...

Homework Statement A wind tunnel is designed to draw in air from the atmosphere and produce a velocity of 100m/s in the test section. THe fan is located downstream of the test section. What pressure is to be expected in the test section if the atmospheric temperature and pressure are -20C...

In the derivation on Wikipedia, it says the following ## \frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}=\frac{dv}{dx}v = \frac{d}{dx}[\frac{v^2}{2}] ## How do they go from the second to last to last equation? I've been trying to understand, but I think I'm just looking over something incredibly simple.

1. Water is flowing in a pipe at 5ms-1, the end of the pipe is held vertically and discharges into the atmosphere, the velocity of water discharging from the pipe is: a=0.25 b=1.3 c=5 d=25 2. The water in the question above will rise to a height in metres of: a=1.3 b=0.25 c=25 d=13 I will be...

What happens when you have more than one hole in a vessel containing liquid? Can you help me finding the velocities at different holes if they are at some height from level of liquid at a particular instant? I know what happens when you put a small hole in a tank containing liquid at a height h...

1. A sphere 1 ft in diameter is moving horizontally at a depth of 12 ft below a water surface where the water temperature is 50F. Vmax = 1.5Vo, where Vo is the free stream velocity and occurs at the maximum sphere width. At what speed in still water will cavitation first occur? Given: speed...

Hello, I am having trouble understanding collision frequency in following discussion from Kubo, $$collision\ frequency = \frac{1}{\frac{l}{v_{x}}}=\frac{p_{x}}{ml}$$ What am I missing ?

I find it hard to believe that the only factor important in computing aircraft lift is Bernoulli's principle. Doesn't good old Newton's Second Law play an effect? In other words simply deflecting the airflow downwards. Does anyone know the relative importance of these factors? (EG for a...

Homework Statement A pump forces water at a constant flow rate through a pipe whose cross-sectional area, A, gradually decreases. At the exit point, A has decreased to 1/3 its value at the beginning of the pipe. If y= 60 cm(the distance from point 1 to the exit, where point 1 is where y=0)...

I was watering my garden the other day, and I noticed (obviously), that the water came out of the hose faster if I stuck my thumb at the end of the hose. Then I suddenly remembered that in physics class, I was taught that gravity-powered water pressure should result in an exit velocity which...

Homework Statement Hi! The problem states: Water through a certain sprinkler system flows trhough a level hose connected to a nozzle which is directed directly upwards. The water leaves the nozzle and shoots to a height, h, before falling back down again into a pool. The hose is connected to...

[SIZE="4"]Definition/Summary Bernoulli's principle is a conservation principle along any streamline of an inviscous flow. It can be expressed as conservation of different types of pressure (force per area) or as conservation of different types of energy per mass. Bernoulli's equation for...

Hi there, I'm having a problem behind the theory of bernoulli's theorem. Can it be applied in an application where water flows from a pump into a pipe with x diameter and out of a nozzle with y diameter to atmosphere. There is a pressure gauge on said pipe. There is a nozzle screwed into this...

Hello, I need some help understanding Bernoulli's principle, flow rate, velocity and pressure. I understand that when the diameter of a pipe decreases, the velocity will increase and the pressure will decrease. But I am having a hard time applying this to a practical application. For...

So I'm not OK with how some people derive this equation. These people consider a pipe whose endings have cross-sectional areas and heights which are different. They then use the conservation of energy principle by saying dW = dK + dU (Where W is work, K is kinetic energy, and U is potential...

Hi, I haven't done many problems of this nature so there are a few steps in my working that i'd like to check are acceptable/agree with what the question implies. Homework Statement A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage...

Bernoulli's with Resistances -- model flow between oil filters Hey guys, It's been a while since I was in school and practicing this stuff daily, so bear with me please! I'm a BSME and I want to model up flow between oil filters. Currently we use a single oil filter with the same pump...

I have attached the geometry of interest with some parts of the solution. The geometry is a vessel that is half of a sphere with an orifice at the bottom. The first expression that they have written, the "A*(2*g*z)^0.5=..." is from conservation of flow rate. 2*g*z is the velocity at the...

hello everyone, I am preparing myself to do the Bernoulli's theorem experiment using the apparatus and I want to go to class knowing what I'm doing and how things work. I'm looking online to find how the apparatus works but I can't find anything. I was wondering if maybe one of you could help me...

Homework Statement What gauge pressure in the water mains is necessary if a fire hose is to spray water to a height of 25 m? Homework Equations Bernoulli's equation(?) The Attempt at a Solution I tried figuring out what water velocity was needed to make the water spray up 25...