Streamline Definition and 21 Threads

The situation is like this: we have a bath of a square cross-section. The cross-section is modeled by an area ##\{x, y: 0\leq x\leq 1, 0\leq y\leq 1\}## in 2d Cartesian coordinates (the gravity fied direction is opposite to the y-axis). There is a hole in the floor of the bath, it starts at...

Hi guys, in the derivation of the Euler equation we apply Newton's 2nd law to a gas flowing through a streamline. To do so, we consider a "box" with sides ##dx## ##dy## and ##dz##: as such; Here, with reference to the image, I can't understand where does that '##+dp##' comes from, and hence...

What forces act at air particle at curved streamline, looking from inertial and non-inertial frame of reference? (show free body diagram)

What is the difference between streamlined and steady flow? Is unsteady streamlined flow possible? If yes, could you please explain what are the characteristics of unsteady streamlined flow?

Hi all, I have attached an image of a page out of the book I am using for context. The blue arrow in Figure 12-3 describes the motion of the particle. I figured the net force would need to be in the same direction, but apparently the net force opposes the motion. So, in Figure 12-3 the pressure...

Homework Statement Use a CV analysis to show that an element of fluid along a streamline gives \[\partial p/\partial x=-\rho u\partial u/\partial x\] Homework Equations \[\sum F=\oint_{CS}^{ } \rho \overrightarrow{V}(\overrightarrow{V_{rel}}\cdot \overrightarrow{n})\] The Attempt at a...

When deriving Bernoulli's equation from Navier Stokes, how do we know it is only valid along a streamline? At the very end of my derivation, assuming Newtonian, incompressible, inviscid, irrotational flow I have ##\nabla(\partial_t \phi + |\vec{u}|^2/2+p/\rho + g z) = \vec{0} \implies \partial_t...

1. Homework Statement As above Homework Equations Not sure. The Attempt at a Solution I've only ever seen one of these problems and it was in the form of V=Axi-Ayj, so much simpler and even then it was poorly explained by the lecturer. I understand what a velocity field is but not much more.

Homework Statement A fluid has velocity components of u=[30/(2x+1)]m/s and v=(2ty)m/s,where x and y are in meters and t is in seconds. Determine the equation of the streamline that passes through point (2 m, 6 m) at time t = 2 s. Write the equation in the form y={y(x)}m, where x is in meters...

There is a thread on plunging into water but it doesn't specify how you land. Consider that a man plunges into the water vertically with his toes pointing downwards, streamlining his body to the maximum possible extent. How can you calculate if the person falling will die or not? Rather how can...

Pathline: When you can see a particle with your eyes and the trajectory of the particle. Streakline: When the particle is "invisible" (such as air) and you have to add paint or dye or something similar in order to see its trajectory. Timeline: When a particle has a pathline, except the...

Along a streamline xy = 4, given u = 2x, v = -2y, I was trying to calculate the acceleration at three different points A(1,4), B(2,2), C(4,1), In my lecture notes, it is said that at A, the fluid is decelerating, at B, the acceleration is zero, and at C it is accelerating. However, i got some...

Hey Guys/Girls and thanks in advance Not quite sure this is in the correct forum since its not a homework question, more private study and curiosity lolz! Im trying to evaluate the curvature along the streamline within a hydrodynamic potential field (fluid flow). I have no issue calculating...

Question: Show that for a steady flow with div.u=0, the density is constant along streamlines. I just don't see how to approach this question without Bernoulli's equation, I can see that the Lagrangian derivative of the density is zero but that doesn't specifically show that the density is...

I have a question regarding fluid streamline vector, why is it different from the usual position vector when you take the partial derivative of it in order to obtain the grad of it? For position vector you take partial derivative and obtain the vector along (for say) a curve. But in fluid...

Homework Statement q1. a)Explain the terms stream-tube. b)State the equation of continutity along a stream-tube for an incomperssible fluid. c)A hosepipe with an internal cross sectional area A1 has at its end a nozzle with a hole whose cross-sectional area is A2 (A2<A1). If the...

Hi All I'm having some problem with this question and was hoping that someone could help me with it. I think I have the first two bits but the rest I'm totally stuck For part (ii) I have the complex potential function as (3x^2)/2 - (3y^2)/2 +6y and the stream function as x(3y-6). Is this...

In a linear shear flow with the free surface being a solitary wave, shall this free surface solitary wave profile coincides with a streamline representing the flow? I have plotted out the streamline of the flow. The streamlines look like the profile of a solitary wave. However the streamline...

Hi all! How shall a streamline pattern of a solitary wave look like? I can hardly find people plotting and discussing this, how this is the case? It shall be reasonable to ask for the streamline pattern of a solitary wave, isn't it? If I want to plot the velocity field of the solitary wave...

Hey guys how do you know when will a flow be turbulent or laminar?i came across a question asking what's the flow of the wind on the sail of a sailboat.i thought that since there is the sail to block the wind when the boat is surfing against the wind, the flow will be turbulent but the ans is...

A recently closed thread dealt with the generation of aerodynamic lift, in particular tied to a severe and justified criticism of the "equal transit time"-principle, which often is also called the "Bernoulli effect". However, from what I read, no one showed how streamline arguments can...