Questions tagged [viscosity]

The viscosity of a fluid is a measure of its resistance to flow, or be deformed, stirred, and changed shape.

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Navier-Stokes equation viscosity term

I cannot understand how the term μ$\nabla^2(\vec u)$ is derived. Can anyone help?
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Inaccurate flow rate measurements of an engine diesel fuel due to change of its viscosity

I am measuring the volumetric flow rate of a diesel fuel using "Turbines" flow meter, both in the supply and return fuel lines of an industrial diesel engine (Caterpillar 3512B – coupled ...
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Buoyancy versus viscosity

A common problem in casting is removing the air bubbles that might might be in the mold material, like plaster or resin. This is typically done by degassing--putting the mold material under vacuum to ...
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Dual-medium Plateau-Rayleigh Instability

(This is my first question here so I would really appreciate your guidance on how to use SO better!) I’ve been working on the Plateau-Rayleigh instability for some time and I was considering the ...
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Prove that horizontal velocity component equation $u=Ue^{-ky}\cos(ky-\omega t)$ is valid (Stokes problem) [closed]

I was presented with this question in my fluid mechanics lecture, however I am a bit unsure how to solve it. The problem is as follows: Knowing that the bottom plate oscillates with velocity $u=U\cos(...
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Force required to move a liquid through a specified opening

If I know the rate of a liquid, the density of that liquid, the velocity of the liquid, and the size of the opening. How would I calculate the force required (in PSI) to move that liquid through the ...
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What would be the Stokes hypothesis in a 1D flow?

In this paper, the author derives the Navier-Stokes equation for a Newtonian fluid starting from the Cauchy equation: $$\rho \frac{D\mathbf V}{Dt} = \rho \mathbf{f} + \nabla\cdot\mathbf{T}$$ where $\...
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Is there such a thing as viscous vapor?

I'd like to simulate a scenario where a character suddenly encounters very high air resistance due to volatile vapors that spread and stick around. Is it possible for some type of gas to be viscous in ...
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Turbulent boundary layer: viscous sublayer definition

I have seen different definitions of the viscous sublayer within a turbulent boundary layer, through my searches. Ones say that the viscous sublayer area is for $y \leq 10 * \delta_v$ where $\delta_v$...
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Calculation of velocity of water flowing along inclined plane by applying Navier-Stokes theorem

Assume that water flows along a inlined plane through a circular irrigation waterway. The inclined plane has its bottom length $B=50 m$, and has height $H=10 m$. So the angle of inclination $\theta$ ...
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Questions about Hagen-Poiseuille Equation: Non-constant Pressure Drop?

The Hagen–Poiseuille equation states that the fluid flow rate in a tube is proportional to the pressure gradient across that tube. Mathematically, it's stated here: $$\Delta p=\frac{8\mu LQ}{\pi R^{4}}...
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Question about using dimensional analysis on an analytically derived equation

Say we have the following analytical relationship for a force: Say we want to non-dimensionalise this equation. I would do this by writing: $$F_L = f(\mu, V, R_1, R_2) $$ ... and going from there. ...
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Why is viscous stress a tensorial quantity?

In an incompressible fluid, the viscous stress (in Cartesian) is defined by \begin{align} \tau_{ij} = \eta(\partial_i v_j + \partial_j v_i) \end{align} for dynamic viscosity $\eta$ and velocity field $...
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Velocity gradient in a liquid

When we consider the motion of fluid in terms of many thin layers sliding over each other , we say that layer at a top of a layer forces it to move forward while layer below a layer forces it to move ...
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Terminal velocity of a metal sphere in water

I am trying to figure out the terminal velocity of a metal ball dropped into water or oil. After searching a bit on the internet, I came to the conclusion that I needed to use Stokes' Law and ...
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Change in Surface Tension of Inviscid Flow

If we have a stationary fluid assumed inviscid (and hence zero viscosity), it's well known that since there are no nonzero net resultant intermolecular forces on the fluids molecules, it possess' no ...
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Why are non-Newtonian fluids called non-Newtonian when they follow Newton’s third law?

To my understanding, Newton’s third law states that for every action there is an equal and opposite reaction. Therefor if I punch the non-Newtonian fluid harder, there will be a harder reaction force ...
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Effect of Steam on the viscosity of air

I am curious if the viscosity of a steam-air mixture is less than that of normal air that we breathe in. According to me, the viscosity should decrease as steam has less viscosity when compared to air;...
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Newton's law of viscosity

I saw that, the shear stress between adjacent fluid layers is proportional to the velocity gradients between the two layers. Did someone know references for empirical test for this law?
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Frictional effects in pilot-static probes

For pilot static probes frictional effects are neglected for high velocity measurement, so that bernoulli equation can be applicable. But isn't head loss proportional to square of average velocity, ...
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Why is honey more dense than water?

I think it's because the molecules in honey are more tightly packed than in water. Would this be correct? And the relationship between gravity and pressure in a fluid is that changing gravity then ...
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What is the interpretation of the symmetric stress tensor in laminar flow?

The strain rate tensor $D_{ij}$ is defined as $$ D_{ij} = \frac{1}{2}\left(\frac{\partial v_i}{\partial x_j} + \frac{\partial v_j}{\partial x_i} \right) $$ For a Newtonian fluid the stress tensor $\...
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Does the free surface of a liquid in a rotating frame depend on the viscosity?

If we consider an incompressible, isothermal, stationary Newtonian flow (density ρ =const, viscosity μ =const), is it true that the form of the parabolic free surface in a rotating frame (constant ...
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Do inviscid fluids have thermal conductivity?

Inviscid fluids are an idealization and they don't have viscosity. The no-slip boundary condition DOESN'T apply to them and consequently, these fluids won't display a hydrodynamic boundary layer. I've ...
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Can Stoke's Law of Viscous Force be applied to freely faaling body?

As air is a viscous fluid can we apply Stokes Law to freely falling bodies. By doing this we can see that the velocity of a freely falling body doesn't increase with time but it stops increasing after ...
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What is the speed of an air bubble in the glass?

This question arises from reading the sf poem Aniara, where the trip of the spaceship is compared to the movement of an air bubble encapsulated in a bulk of glass. How fast can such a bubble travel?
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Kubo formula for viscosity tensor

Viscosity tensor in terms of the retarded Green function is as follows : \begin{equation} \eta_{ijkl}=-\lim_{\omega\to 0}\frac{1}{\omega}Im G^{R}_{ij,kl}(\omega,0)~~~~(1), \end{equation} where $G^{R}_{...
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Internal resistance for a fluid flowing in pipe

Lets say we have a fluid moving in a pipe with velocity v. what would be the resistance faced by it? in our class, the professor told us that internal resistance faced by fluid is given by R=8nl/pir^...
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Velocity viscous flow around rotating cylinder

I am struggling to find an equation of flow velocity at distance $r$ around rotating cylinder with radius $R$, angular velocity $w$ in stationary viscous fluid with some density $ρ$ and viscosity $\mu$...
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Vacuum pen manipulation of dies in viscous media [duplicate]

I'm using a vacuum pen to lift a die and manipulate it in an epoxy pool. The die is slipping off the tool as the viscosity of the epoxy may be too large. I need to design a new vacuum tool and I like ...
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Stress-strain relationship for linear viscoelastic solid

I am a bit confused about the definition of a linear viscoelastic (isotropic) solid. Following Landau and Lifshitz (Theory of Elasticity, section "viscosity of solids"), I would say that in ...
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Shape evolution of a fluid jet exiting a sharp hole in the bottom of a container

Imagine we wish to model the evolution of the diameter of a fluid jet exiting vertically downward from a large tank through a sharp-edged hole in the bottom of the tank, under the influence of gravity ...
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How identify from velocity values, if a flow is viscous or inviscid?

So in my Fluid Mechanics classes we need to know how to identify viscous flows from inviscid ones, using Matlab, and only with velocity values. How can I know de difference? An example is pictured in ...
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Physical Meaning and/or Justification to $\lambda = 0$ Case for Compressible Navier-Stokes

I am looking for information on the coefficient $\lambda$ in the following formulation of the barotropic compressible Navier-Stokes system: \begin{align} & \partial_t \rho + \text{div}(\rho u) = 0,...
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Regarding direction to take gradient in shear force calculation

So I was solving a problem on rotating viscometer. In the torque calculation if there is the boundary of horizontal plate at bottom we take the gradient in vertical direction to calculate velocity ...
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Steady Couette flow where the moving wall suddenly stops

Let it be a planar Couette flow for an incompressible fluid with dynamic viscosity $\mu$ and density $\rho$ that has reached the steady-state. Assuming that the plates are placed at the $xz$ plane, ...
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Is Viscosity due to adhesive forces or cohesive?

So if a non-ideal fluid is in motion, in a siphon for instance, then I completely understand why viscosity could arise due to cohesive forces between the particles. But let's say we drop a metal ...
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What is the molecular underpinning of pressure in fluid mechanics?

The Navier-Stokes equation tells us that there are two ways of transferring momentum to an infinitesimal volume of fluid through the action surface forces: (1) pressure and (2) viscous stress. On a ...
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Dive into a pool of mayonnaise. What happens next?

First, some train of thought to show I am not completely insane. Last night there was a college football bowl game, the Duke's Mayo Bowl. I naturally assumed the winner would receive a lifetime ...
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Kelvin's Circulation theorem

Recently, I dipped my spoon into my tea. I saw that as I dipped my spoon into my tea, two vortices formed at both edges of the spoon. I guess this is similar to vortices forming at the end of ...
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Coefficient of viscosity $\eta=\frac{F l}{v A}$

The coefficient of viscosity is described in my textbook as the ratio of shearing stress to strain rate. However, I am unable to understand how the coefficient of viscosity is derived here based on ...
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Why d'Alembert's paradox has zero drag?

Why d'Alembert's paradox has zero drag? Even if viscosity is zero why drag is zero if there is no stagnation pressure at the back (right) side of ball? Why flow stay attached to ball surface,even ...
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Viscous flow over a perfectly smooth surface

Can a viscous liquid flowing over a hypothetical perfectly smooth surface exert viscous stresses on the surface? Can the viscosity of a fluid describe interactions between the fluid and some other ...
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What does $ \mu \nabla^{2} \vec V$ mean in the Navier-Stokes equations?

$$\rho\frac{D \vec V}{Dt}=-\nabla p+ \mu \nabla^{2} \vec V+\rho g$$ In the Navier-Stokes equations there's this term $ \mu \nabla^{2} \vec V $. I don't really understand what this means. What is the ...
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Why can't water flow fast when the impact speeds up? (the incompressibility)

I'm a high school student studying physics in Korea! Please understand my poor English skills. In the text below, the liquid is said to be destructive and incompressible. And he says, "I the ...
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What was the need for defining kinematic viscosity?

How is kinematic viscosity physically different than dynamic viscosity? What was the need for defining a new quantity ie kinematic viscosity though one can get one from the other? Do try to give a ...
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Stoke law determend the viscosity of liquid

In an experiment to determine the viscosity by the Stoke method. When we throw the ball into the liquid it will reach a certain mark and start recording the time. This mark what determines its ...
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Viscosity in fluids is like kinetic friction between solids. But what is the fluid-equivalent of static friction?

Viscous stress is proportional to $\frac{du}{dy}$, so they only arise from relative motion between different layers of fluid. That makes it somewhat similar to kinetic friction, which requires ...
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Simplified effect of viscosity on flowrate when flowing from a cylinder through a small hole?

I'm writing a high school project and am studying the effect of viscosity on the flow rate when a Newtonian liquid (concentrated sugar with water) flows out of a hole (let's say of radius r << ...
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Test tank physics

In a test tank scaled-down simulation of, for example, a ship stability problem, is it not incorrect to assume that water will behave in a scaled-down fashion with regard to wave period? Don't we need ...
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