Bernoulli equation Definition and 133 Threads

Here is an illustration of something that came into my head: http://imgur.com/a/V9V8S (also attached to question) If we do a energy balance (in terms of head) between point 1 and point 2 (ignoring friction for now, it's not really important): $$\frac{P_1}{\rho g} + \frac{v^2_1}{2g} + z_1 +...

Homework Statement A cubic wine box of dimensional length ##h## has a small tap at an angle at the bottom. When the box is full and is lying on a horizontal plane with the tap open, the wine comes out with a speed ##v_0##. i) What is the speed of the wine if the box is half empty? (Neglect...

I have trouble understanding why we classify an inviscid adiabatic incompressible flow along a streamline as isentropic I understand this from a Thermodynamic definition/explanation $$dS = dQ/T$$ Adiabatic Invsicid $$dQ =0= dS$$ So no heat added or lost no change in entropy I'm fine with that...

I have a diagram similar to the following. Water entering the larger end is at 20degreesC. The larger end has a diameter of 8cm and Area 50.26cm2. The small side has a diameter of 3cm and Area 7.0685cm2. The water jet exerts a force of 87N on a flat plate at an unknown distance. Assuming no...

Homework Statement What gauge pressure is required by city mains for a stream from a fire hose connected to the mains to reach a vertical height of 15m? Homework Equations Bernoulli Equation: The Attempt at a Solution

Hi boneh3ad Your discussion on Bernoulli Equation was very impressive and helped me a lot to understand this rather complicated equation. I have a question which puzzles me a lot when I want to solve it using Bernoulli equation. Here is the statement. " If there is some fluid flowing thru a...

Hi PF! I was reading about Bernoulli's equation for steady, inviscid, incompressible flow. Now it's my understanding this equation is derived from the Navier-Stokes (momentum balance); then these two equations are identical regarding information offered. However, while thinking about...

The problem statement Example 1 A single particle I have a particle being forced by a radial centripetal force onto a smaller radius $$l_1=m_c.v_1.r_1$$ $$L_1=L_2$$ $$L_2=m_c.v_2.r_2$$ $$m_c.v_1.r_1=m_c.v_2.r_2$$ $$v_1.r_1=v_2.r_2$$ $$v_2=v_1\frac{r_2}{r_1}$$ Its increase from ##v_1## to...

Homework Statement [/B] A simplified schematic of the rain drainage system for a barn is shown in the figure. Rain falling on the slanted roof runs off into gutters around the roof edge; it then drains through several downspouts (only one is shown) into a main drainage pipe M below the...

Homework Statement I would really appreciate it if you could give me a hand with this exercise, not sure on what I've done. Data: Moody: L=55*10-3m D=10-1m k=0.0002m Homework Equations ##Re=\frac{D*u*ρ} {μ}## ##Re=\frac{4*m} {pi*D*μ}## Relative roughness ##ξ=\frac k D## where k=rougness...

Homework Statement Hello,Could you please lend me a hand with this problem?I would really appreciate it. Question:[/B] Their Answer: KL=2*0.75(2 elbows) D=5*10^-2 m ;f=0.001(fanning friction factor) Assumptions I made: Point 1 which is at the top of the liquid in the tank: h1=23 m...

Hello everyone, The boundary condition : P=0, z=ζ is very common when studying irrotational flows. When cast with the Bernoulli equation, it gives rise to the famous dynamic boundary conditionn, which is much more convenient : ∂tφ+½(∇φ)2+gζ=0, z=ζ But what happens if the motion is rotational ...

consider ODE : Show that the solution to this ODE is: Can someone tell what kind of ODE is it?I thought,it's on the form of Bernoulli ODE with P(x)=0.Is it possible to still solve it by using Bernoulli Methodology?I mean by substituting u=y^1-a with a=2? Thanks

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...

I have a doubt on the use of Bernoulli equation for pumps. Consider the situation in the picture. I marked different points: ##1## on the surface of first tank, ##2## in the exit from first tank, ##3## just before the pump, ##4## just after the pump and ##5## entering the second tank. Now...

Homework Statement The train is traveling in a gallery at ##v=70 km/h##. Outside air is not moving and pressure is ##p_0=101325 Pa## and temperature ##T=283 K ##. The area of the face of the train is ##A=9 m^2##. Determine the minimum area of the section of the gallery such that the pressure...

Homework Statement A well-fitting piston with 4 small holes in a sealed water-filled cylinder,shown in Fig is pushed to the right at a constant speed of 4 mm /s while the pressure in the right compartment remains constant at 50 kPa gage. Disregarding the frictional effects,determine the force...

Homework Statement [/B] Suppose we have a u-shaped tube filled with water, with oil added at one end which disturbs the equilibrium. Now say one end is blocked off and the other is exposed to air flow which reduces the pressure above the water and causes the water to climb back to equilibrium...

Hi I am having trouble understanding how Bernoulli’s pressure gradients develop I know the equation in a steady flow state (after the developed state ‘flushes’ thru) but I want to understand what mechanism lowers the pressure and increases the speed as the flow develops The continuity...

Homework Statement Hi everybody! Here is a classical Bernoulli problem, which I'd like you to review to check if I (finally!) make a proper use of Bernoulli's equation! A gardener waters a bush with the help of a watering can (see attached pic). The water level in the can lays at height H =...

What i know is that the Bernoulli equation is applied only along a streamline. Is it correct to say that eductors work on the Bernoulli equation?

Hi everybody! I'm training for an upcoming exam, and I'd like to know if I correctly use the Bernoulli equation. Homework Statement The problem is kind of difficult to describe without a drawing, please check out the attached jpg to see the situation and the known data. The questions are: a)...

Based on the law of mass continuity, when a pipe narrows then the speed of the fluid increases. Then why is it that when draining a tank the speed of the fluid only depends on the height of water above and not on the size of the hole? Wouldn't a narrower hole mean that that the speed must be...

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...

Homework Statement Water flows from the faucet on the first floor of the building shown in the figure with a maximum velocity of 20 ft/s. For steady inviscid flow, determine the maximum water velocity from the basement faucet and from the faucet on the second floor. Assume each floor is 12 ft...

Homework Statement It is time for aged physics lecturers to have their flu shots but even that can be interesting. Assume the density of the vaccine in the syringe is the same as the density of water. The diameter of the syringe is 6mm, the length of the needle is 3cm and by reading the packet...

I am planning to build a Hero's steam engine or Aeolipile. This is the steam engine invented by the Greeks about 2000 years ago. It is attributed to Hero or Heron (10-70 AD) but was also referred to in 15 BC. My grandfather build one for a show. I have inherited it but rather than try to repair...

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...

(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...

< Mentor Note -- please remember to use the Homework Help Template when posting schoolwork questions >[/color] Consider the fully developed laminar flow due to gravity of water in a vertical circular tube. Assume atmospheric pressure at inlet and outlet. Show that the relationship between...

Dear Everyone, I need someone to check the solution, The question identity and then solve, The Equation is Bernoulli To Solve: $(ye^{-2x}+y^3)dx-e^{-2x}dy=0$ $\frac{1}{dx}(ye^{x}+y^3)dx=\frac{1}{dx}(e^{2x}dy)$ $ye^{-2x}+y^3=e^{-2x}\d{y}{x}$ $e^{-2x}y^{\prime}-ye^{-2x}=y^3$ Let...

Considering horizontal flow in a pipe (under the action of pressure forces only) if we focus on a fluid element we have a pressure gradient across the same i.e, a net pressure force will always act over the element that essentially maintains the flow.Now, in a region in the flow field if the...

Referring to the problem in the attachment, the author mentions that if we consider the coordinate system attached to the bicycle and the bicycle accelerates or decelerates, the flow past the bicycle becomes unsteady. For an unsteady flow, we know that nothing changes at a given location on a...

Homework Statement The photo below shows a stream of water in steady flow from a kitchen faucet. At the faucet, the diameter of the stream is 0.960 cm. The stream fills a 0.125cm3 container in 16.3 s. Find the diameter of the stream 13.0 cm below the opening of the faucet. Homework Equations...

Hey everyone ! I'm new here and found that this forum was very useful. Would really appreciate it if you could help me out with this problem ! Have been scratching my head for hours now :( Question: Thank you very very much once again !

Why is the water level in the object above the water level of the current? How to apply Bernoulli equation in this case?

Homework Statement Find the general solution: y'-3y=(y^2) Homework EquationsThe Attempt at a Solution divide both sides by y^2 y'(y^-2) -3(y^-1) = 1 we know v=y^(n-1) v=y^-1 v'=d/dx(y^-1) v'=-(y^-2) y' plug it back into y'(y^-2) -3(y^-1) = 1 -v'-3v=1 this is where I think I am making a...

Homework Statement Homework Equations P1+pV12/2+pgh1=P2+pV22/2+pgh2 The Attempt at a Solution My thinking: since the pitot tubes measure the stagnation pressure (static + dynamics pressure) and the height of the tubes are the same. By Bernoulli's equation, the total pressure along a...

Hi! I am having trouble following the derivation from Euler's Equation to Bernoulli's Equation. The trouble lies in the math, not the physics part. Especially the step when partial derivatives are being integrated. I have attached the relevant part as a screenshot. How does the...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Here is the question: I have posted a link there to this thread so the OP can view my work.

Hello! I have the following Bernoulli equation: 2xyy'+(1+x)y^2=e^{x} , x>0 lim_{x -> 0^{+}} y(x) <\infty The transformation is u=y^{2} . So, u'+(\frac{1}{x}+1)u=\frac{e^{2x}}{x}.How can I find the initial value u(1) so that lim_{x -> 0^{+}} u(x) <\infty ??

Hey! So if the vorticity of a fluid = 0, it is in steady state laminar flow and friction is negligible (and viscosity too?), you can use the bernoulli equation between any two arbitrary points in the fluid, regardless if they are connected by a streamline. If the vorticity is non-zero, can...

Here is the question: Here is a link to the question: Determine the solution to the following differential equation.? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Homework Statement Can anyone tell me why, in the figure attached, the pressure in the manometer at 1 is a stagnation pressure? I understand that you get stagnation pressure at a stagnation point but point one is below the stagnation point, not on the stagnation point. Therefore how can it be...

Homework Statement Please help me as I am quite confused in Bernoulli's theorem derivation...In my textbook,it is considered that Fluid Moves from a Greater height h1 to lower height h2,The pressure on upper end is positive,while at the lower end,it is negative,i.e against the motion of...

Thermodynamics -- Bernoulli Equation question "The Bernoulli Equation is restricted to frictionless incompressible fluids, the S.F.E.E is not".? Explain the fact ?

Hi, I am a first year studying mechanical engineering and I am having trouble understanding bernoulli equation. This is the first question in the tutorial and I can't seem to get the right answer. Water flows through the pipe contraction shown in the figure below. For the given 0.2 m...

Hi PF! I've been working on a research problem involving fluid dynamics, and I'm currently looking at a "bathtub flow". This is where water is draining through a hole, and we have a vortex. In a paper I have found dealing with this flow, the velocity potential was written as: \psi = Alnr + B\phi...