Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.:3
It has applications in a wide range of disciplines, including mechanical, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology.
It can be divided into fluid statics, the study of fluids at rest; and fluid dynamics, the study of the effect of forces on fluid motion.:3
It is a branch of continuum mechanics, a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a macroscopic viewpoint rather than from microscopic. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems are partly or wholly unsolved and are best addressed by numerical methods, typically using computers. A modern discipline, called computational fluid dynamics (CFD), is devoted to this approach. Particle image velocimetry, an experimental method for visualizing and analyzing fluid flow, also takes advantage of the highly visual nature of fluid flow.
The discharge coefficient is the ratio of the actual discharge to the ideal discharge and can be measured experimentally. If one were to experimentally measure the discharge coefficient using water, would this value be constant for all incompressible fluids?
What does the discharge coefficient...
Do you know of any place where I can look up things about the momentum (linear momentum) in fluid mechanics? It's just that when I have a variable velocity and it has to be integrated, I don't quite understand how to do it.
I have looked for videos and things and I can't find that they are...
I was looking at an example of fluid mechanics and I don't understand this.
Statement figures:
CONTINUITY EQUATION
$$\left. \dfrac{dm}{dt}\right]_{MC}=(\dot{m}_2+\dot{m}_3)-\dot{m}_1=0$$
$$\dot{m}_1=\dot{m}_2+\dot{m}_3$$
$$\rho c_1A_1=\rho c_2A_2+\rho c_3A_3$$
$$\rho c_1 h1=\rho c_2...
I think in the explanation below a very small element of the liquid at the line of contact between the horizontal solid surface, air outside the liquid and the liquid itself is being taken, and forces acting on such a small element are being shown. This very small element is to the left of shown...
According to what I get, the problem clearly says that ##p_2= 500 ## kPa. I can also see that ##p_1 > p_2## since higher velocity means lower pressure in a flowing liquid and we can say that ##v_1<v_2##.
Basically the air works like a spring, it always tries to get back to its resting state. And it's like Hooke's law, the more it deforms the more elastic potential energy it has. That's why the faster you are, the air resistance is greater. Thinking in this way, I imagine that in fluid mechanics...
Hello, I am currently studiying Bernoulli's equation and I have trubble understanding something , say we have a horizontal hose (no change in altitude of pressure ) Bernoulli's equation state that an ideal fluid can flow thought the hose with the same velocity , does an ideal fluid need a...
hello, I read in a lecture paper about fluid mechanics that velocity is not related to viscosity, i found this odd and i think it is an error , can someone confirm that?
The general balance equation is as follow: d[m{u+gz+v2/2)sys=(u+gz+v2/2)dmin-(u+gz+v2/2)dmout +dq+dw.
I understand that I would take in consideration the cross sectional area as well as the mass flow rate. However I can't figure out what else to consider as if atm pressure should be considered...
Hi everyone,
I just started graduate school and I've been working in an experimental fluid mechanics lab. We have a shock tube and run tests on studying supersonic and hypersonic airflow under different conditions. We use Schileren imaging and transducers to take measurements during tests. We...
A cylindrical tube (diameter = D, width = L) is completely filled with a liquid (density = ρ). A pump pressurizes the system with a pressure P. Consequently, 1) the solid tube is compressed and deformed according to Hooke's law (σ = ε.E), and 2) the liquid is compressed and deformed, following...
Hello!
I have a question about aerodynamic drag. It sounds simple but when trying to understand why the relative velocity can be used in calculations I have some trouble. The formula is 0.5*rho*u2*cd*A where u is the relative velocity between the object and the fluid. The cd value depends on the...
I have read about doppler effect in acoustics so i searched for the relation ship between wavelength of wave produced by linear movement of body and its momentum along with other dependent variables such as density of fluid (leaving acoustics for a second) and temperature but souldn't find a...
They say that a rotating knife thrown is more dangerous than a knife thrown straight
I find it weird
If the knife is rotating, it will experience more air drag than if thrown straight which will also depend on plane of rotation(For some reason, I don't know, it experiences more drag if...
Hey all,
I recently took an aerodynamics exam that included the question "Please Explain how the Bernoulli Equation can be Applied Inside a Boundary Layer". Now, it is my belief that the Bernoulli equation, defined by my textbook as P+0.5ρV2=ℂ, requires inviscid flow to be properly applied...
Hey everyone,
I'm coming to the end of my Mechanical Engineering B.S. degree and I've been in the process of applying to mechanical and aerospace PhD programs. I want to do research in fluid mechanics; I have some expereience in hypersonics from a Research Expereince for Undergraduates NSF...
I can't seem to find the arclength between A and B.
I tried using L = integral (0.6 to 0.4) of sqrt (1+ (dz/dx)^2) to no avail.
Would it be roughly similar to 400 km (the length from A to B) since the change in elevation could be considered negligible? Furthermore, how might I go about...
I’m trying to calculate the weight I have to support at one end of a pipe with flowing water. So suppose you had a water pipe that extended from the ground upwards some distance away both horizontally and vertically, i.e., at an angle. Normally, you don’t have to worry about this issue because...
(a) Write down an expression for the velocity field corresponding to uniform
rotation. Find the vorticity corresponding to this flow.
(b) Consider a small perturbation u' to the state of uniform rotation with angular
velocity Ω, which has the form of a plane harmonic wave
u'= A exp i(k·x−ω t) +...
Dear physics forum dwellers,
Currently on search for an advanced fluid mechanics book that covers all the nitty gritty details. Not looking for general introduction books like Munson, Rothmayer, ... or Cengel that are used in bachelor physics classes or engineering classes. Even after skimming...
Summary:: What is the best way to get into the Aerospace Engineering Industry?
Hi everyone,
I'm new to the physics forums. My name is Andrew, I'm going to be in my undergrad Senior year in mechanical engineering this coming fall. I've recently been looking into PhD programs and I've been...
This is actually right at the start of another derivation, but I can't understand how the author gets the formula for ##q##. So the discharge per unit thickness is the circumference of the circle, multiplied by the velocity at that point (at ##r##)? I thought the formula for flow rate was...
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##...
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 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...
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...
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.
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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=...
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)...
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...
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...
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...
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...
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...
Dear all,
recently I read in a belletristic book about Reynolds Vortices. In the fictitious story the author writes about special (Reynolds) vortices generated in the whitewater, which can be passed in only one direction by objects of a "critical" density, which then will be kept in the vortex...