Fluid mechanics Definition and 758 Threads

Here is the setup: Apply Bernoulli Principle to the top (free surface) of the two pitot tubes (1 for static and 2 for dynamic with the points colored in red): $$\frac{p_1}{\rho_w g}=h+\frac{p_2}{\rho_w g}$$ The difference in air pressure would give the following:$$p_1=p_2+h\rho_{air} g$$...

Assume the jet is straight but the radius of the jet varies over it's length (like a jet of water falling which narrows due to gravitational acceleration). Also ignore viscosity. A pressure gradient would be required to accelerate the fluid radially. Because during an expansion transformation...

According to one explanation, the left hand acceleration terms of Navier Stokes equations are the called the inertial terms. If you were to balance forces on the fluid particle, they would have to be equal and opposite to the forces on the right hand side (pressure gradient, viscous, and body)...

When figuring out the capillary pressure on a liquid in a tube of a certain cross-section, the typical approach is to consider the Young-Laplace pressure and the curvature etc. I was looking through some of my old notes and I had an equation for the capillary force: fc = γ cosθ dS/dx where γ...

A water drop of radius ##10^{-2}## m is broken into 1000 equal droplets. Calculate the gain in surface energy. Surface Tension of water is ##0.075 ~N/m##. So, for the solution of the above problem we need to know how much surface area (combining all 1000 droplets) have increased from the...

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...

Let’s say we have a unit volume of some fluid in a column on the Earth surface. Let ##\mathbf F## be the gravitational force that acts on the unit volume of the fluid. Consider a small volume element ##\Delta \tau## in the fluid and let’s assume it to be a cuboid with dimensions ##\Delta x##...

I figured out stokes law equation but I am unable to proceed further

Elemental fixed streamtube control volume from Professor White’s textbook “Fuid Mechanics”: I was unable to develop the intermediate steps for the following approximations: (continuity equation according to the book ) Where and (Momentum equation according to the book) In...

Let’s say we have a boat whose longitudinal axis is the y-axis (which goes into the screen in the figure below) standing upright in a still water . ##S## is the Center of Mass of the boat and ##C## is the Center of Mass of the displaced water.On ##S## lies the force ##\mathbf W##...

A reservoir supply tunnel transfers water from a high level storage reservoir via a 200mm diameter pipe to a lower intermediate reservoir. The total height difference between the free surfaces of each reservoir is 76 m. The pipe is 700 m long and the coefficient of friction, Cf is 0.009. The...

In Sommerfeld’s Lectures on Theoretical Physics, Vol II, Chapter 2, Section 6, Page 43 we derive an expression for the equilibrium of liquids as $$ grad ~p = \mathbf F$$ Where ##p## is the pressure and ##F## is the exertnal force. Then he writes, [ The equation above ]includes a very remarkable...

I am working on a project where I have to calculate various results relating to the motion of a water bottle rocket being launched. I am currently stuck on trying to find how long the thrust period of the rocket is. The model for the rocket is as follows: It is a 2L (0.002m3 bottle filled with...

I researched the solar collectors implemented in practice for water detoxification and I found out that the preferred design is the Compound Parabolic Concentrator. Knowing that I have no information regarding radiation beyond what's taught generally in heat transfer courses in chemical...

By Fluid Mechanics I mean the mechanics of fluids, both at rest and in motion. I'm unable to find introductory books on Fluid Mechanics which contains everything in itself, for example I downloaded Fundamentals of Fluid Mechanics by Munson, Young, Okiishi, Huebsch and I don't know why but I...

Can someone please tell me what is the name of below formula? ##H = z + \frac{v^2}{2g} + \frac{p}{γ}##

Can anyone suggest me a Fluid Mechanics textbook? I am currently in High School in my Junior Year. I am looking for a entry-level textbook so I will be able to solve I.E. Irodov's Hydrodynamics section. (My Mathematics is quite strong)

Homework Statement: An open tank with a rectangular side 1 m wide and 4 m high is filled with a liquid of variable specific weight, γ, with γ = 50 + 2y (N/m3), where y is measured vertically downward from the free surface. Find the magnitude of the force on the side of the tank. Homework...

Hi, I am a high school student doing a project on fluid dynamics and need to understand the relevant maths so that I can understand how to apply the mathematics of fluid flow (particularly air flow around a cylinder). I have a basic calculus understanding and need to understand the navier...

Summary: I have been looking around and trying to understand what the physical use is for a streaklines. While we are at it, maybe we can discuss how they differentiate from pathlines, streamlines and timelines as well as discussing their uses. Thanks for your feedback in advance. .

Homework Statement: how far from the mercury surface must a horizontal line be drawn in a 2 meter square gate whose one side is at the fluid surface so that the hydrostatic forces in the two newly formed surfaces are equal Homework Equations: 1) F = yAh where y= specific weight A is the cross...

Tom Crawford (sporting a Navier-Stokes tattoo) talks about the famed equations - subject of a $1m Millennium Prize.

Problem Statement: I am having trouble deriving the expression from the initial equations. (Calculate the emptying time considering Volume conservation) Relevant Equations: Q=A*sqrt(b(H-h(t)) And we have dh/dt =Q/S (conservation equation) and we have to obtain h/H = 1-(1-t/te)^2 with te=...

Problem Statement: There is no precise problem statement since it's an homework to be done independently, but I will try my best to explain it concisely (I also apologize for my mistakes in English) : I want to reproduce the simulation of the model presented in the pdf file attached to this...

Does the definition of fully developed flow is different for laminar and turbulent? I understand the fact that the entrance length are different in laminar and turbulent flows, but I believe the definition of fully hydrodynamically developed flow means that the velocity profile (hence momentum)...

Problem Statement: An oil with density 900 kg/m3 and viscosity 0.18 Ns/m2 flows through a circular pipe which inclines upwards at 40° to the horizontal. The length of the pipe is 10 m and the diameter is 6 cm. The fluid pressure at the lower end of the pipe is 350 kPa and the pressure at the...

So when the velocity of v1 and v2 is 0 (because the tanks are much bigger), the bernoulli equation to dh is dh = (dp-dpl)/(rho*g) with dp = Phyd / V = 1000W / 0.01m³/s = 10^5 Pa and rho = 1000 kg/m³ So I am getting first without the pressure loss on the orifice dh = 10^5 Pa / (1000 kg/m³ *...

i really can't understand the answer of this question, is the question 1.3 in fluid mechanics by Frank ,M White For the triangular element in Fig P1.3, show that a tilted free liquid surface, in contact with an atmosphere at pressure pa, must undergo shear stress and hence begin to flow. i...

So if we define point 1 at the entrance and point 2 at the exit, then we can write out Bernoulli's equation along a horizontal streamline as such: p_1 + \frac{1}{2}\rho v_{1}^2 = p_2 + \frac{1}{2}\rho v_{2}^2 = p_{atm} One question is: won't there be p_atm also contributing to the static...

For this question, this is my working. The main issue is I cannot figure out where the factor of \frac{1}{2} comes from. So I consider a control volume right around the propeller (in the frame of reference of the propeller) and I apply R(-->) Force = Change in Momentum Flux F = \dot{m_{o}}...

I am not really worried about the numbers, but more about the simple concepts with head loss in these pipe flow questions. I want to confirm that head loss just means the change in static head, right? I have been advised that for a problem like this, it is nothing more than the conservation of...

Some thoughts that I've had on the question are saying the volume flow rate (##Q##) in, must equal the volume flow rate out. If that's the case, then: ##Q_{in} = Q_{out}## ##A_1V_1=A_2V_2## But... no areas have been given. And height doesn't enter this equation at all. Then I thought it...

1. What should be the size of object/Particle (sphere) so that it should remain suspended (neither it should sink nor it should float)? container dimensions 30*25*25, density of fluid 0.9g/cm3 , density of particle 0.86g/cm3 , particle is coated with aluminium having density of 2.07g/cm3.(if...

1. A 20-lbf disc with diameter 18" and thickness of 3" is held static while completely submerged in water. Upon release of a lock, the disc experiences a torque from a torsional spring that causes rotation about its center of mass along the x/y axis (think coin toss, not wheel). If the spring is...

Homework Statement A drop of water fall towards the ground with initial mass [m][/0] and radius [r][/0] (assume the initial shape of that water drop is sphere). the air resistance is F=½.ρ.A.[v][/2].C (C is the drag coefficent, A is the area that the air contact with the water drop and ρ is the...

Hello! I hope you are all doing well! I've been always intrigued by fluid mechanics and decided to try out a quick experiment with my water faucet. After using some equations I found online [1] [2], I plugged a hose to the faucet and let the water run. I filled a 1 quart bowl and recorded the...

Hi all! I have started reading Fluid Mechanics at my own pace (no university study) and really I would like to grasp the ideas behind it. So I have Fluid Mechanics by Cengel - 4th edition. At page 45 the coefficient of compressibility or bulk modulus of elasticity (κ) is introduced. ##κ =...

Homework Statement [/B] Homework Equations ##P=\rho gh## The Attempt at a Solution So this is the first time I'm doing fluid mechanics, and I'm trying my best to understand it. This was the first question, and truth to be told, I'm not very confident. I know what gauge pressure is: the...

Hello, I am trying to understand the maths/physics/chemistry behind this situation. Here is the scenario. I have 8 grams of pressurized N2O in a cylinder at 60 bar/ 900 psi. If the temperature stays constant (let's say 50-70°C, or at a temperature where the N2O can stay as pressurized as...

Can an expanding balloon be considered a control volume?

Hi all, Ameya here from the University Of Twente Netherlands pursuing masters in electrical Engineering. Currently doing my thesis. My topic involves developing a biomimetic sensor.

I am trying to determine a normal stress balance at an axisymmetric and dynamic fluid-fluid interface, ##z(r,t)##. For a static, free surface, this simplifies to the Young-Laplace equation: $$ \Delta p=\rho gz-\sigma2H=\rho gz-\frac{\sigma}{r}\frac{\partial}{\partial r}\left(r\frac{\partial...

Homework Statement Find the flow around a cylinder with radius ##a## generated by linear vortex ##\Gamma## in point ##z=b##. Find points of stagnation. Also ##b>a## Homework Equations Complex potential of vortex: $$\omega_{vortex} = \frac{\Gamma}{2\pi i}\ln{z}$$ Milne-Thomson circle theorem...

What does it mean the word 'Jet' in fluid mechanics, special when it depends on the free surface?!

Homework Statement Water is supplied at 4.50 m3/s and 415 kPa (abs) to a hydraulic turbine through a 1.0-m inside diameter inlet pipe as indicated in the figure. The turbine discharge pipe has a 1.2-m inside diameter. The static pressure at section (2), 3 m below the turbine inlet, is 25 cm Hg...