# What gives a liquid energy to flow ?

The pressure difference sure.The point where there is higher energy in order to attain lowest level of energy moves towards region of lower energy, but if this liquid is viscous enough, doesn't the whole energy get lost during flowing? then how is the pressure level or rather the energy level balanced across two ends.

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Andy Resnick
Pressure is not energy- a pressure gradient is associated with changes in momentum. Similarly, viscosity can be thought of as 'diffusion of momentum'- the unit of dynamic viscosity, Stokes, is L^2/T and equivalent to [momentum/density] and is the same as the diffusivity constant in for example, Fick's law of diffusion.

Highly viscous fluids respond slowly to an externally applied pressure gradient because any momentum imparted to the fluid rapidly diffuses from a macroscopic scale to a microscopic scale.

Chestermiller
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The pressure difference sure.The point where there is higher energy in order to attain lowest level of energy moves towards region of lower energy, but if this liquid is viscous enough, doesn't the whole energy get lost during flowing? then how is the pressure level or rather the energy level balanced across two ends.
If you are flowing a fluid through a pipe by applying a pressure gradient, the velocity of flow through the pipe will decrease inversely with the viscosity (for laminar flow), assuming you hold the pressure gradient constant. If you want to keep the flow rate constant, you will have to increase the pressure gradient if you wish to increase the viscosity. None of this should be too surprising.

I think my question here is being mis- interpreted, maybe because of my poor choice of words.
what I would like to say is that #why does a fluid flow from high to low pressure, what makes it flow?the complete picture of what exactly is happening?

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Chestermiller
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Why does electrical current flow through a resistor from high voltage to low voltage?

I think my question here is being mis- interpreted, maybe because of my poor choice of words.
what I would like to say is that #why does a fluid flow from high to low pressure, what makes it flow?the complete picture of what exactly is happening?
Consider a free body diagram applied to an arbitrary volume inside the fluid. You will see that the pressure differential leads to an imbalance of forces on that volume, resulting in acceleration and thus movement of fluid.

Consider a free body diagram applied to an arbitrary volume inside the fluid. You will see that the pressure differential leads to an imbalance of forces on that volume, resulting in acceleration and thus movement of fluid.
clear enough, just one doubt? the pressure at a particular point is isotropic, so the pressure acts in every direction but it flows only in one? is it because on other sides the pressure is balanced?

Dale
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clear enough, just one doubt? the pressure at a particular point is isotropic, so the pressure acts in every direction but it flows only in one? is it because on other sides the pressure is balanced?
Saying that the pressure is isotropic at a point is a little strange. Pressure is a scalar, and I have never heard anyone describe a scalar field as being isotropic at a point.

However, it isn't pressure that causes the flow, it is the pressure gradient (what DocZ called pressure differential). The pressure gradient is a vector field, so it has a direction at each point.

To follow up on the pressure gradient, I worked out what I thought might be a sensible expression for the acceleration of fluid:

First I considered that a fluid would want to flow in the direction of pressure decrease, so I took the negative gradient. I then divided by fluid density to get units of acceleration...then I added the acceleration due to gravity and got the following. Is that about right?

$\dfrac {-\nabla P(x,y,z)} {\rho }-g\widehat {j}=\overrightarrow {a}$

Chestermiller
Mentor
Saying that the pressure is isotropic at a point is a little strange. Pressure is a scalar, and I have never heard anyone describe a scalar field as being isotropic at a point.

However, it isn't pressure that causes the flow, it is the pressure gradient (what DocZ called pressure differential). The pressure gradient is a vector field, so it has a direction at each point.
Actually, in fluid mechanics, the isotropic portion of the stress tensor is equal to the (scalar) pressure times the metric tensor. This is why people sometimes say that the pressure is isotropic. In cases where the (viscous) deformational portions of the stress tensor are negligible, the stress tensor becomes essentially isotropic, and equal to (minus) the pressure times the metric tensor: σij = -p gij. In a differential force balance on a parcel of fluid, the force per unit area on a portion of the surface of the parcel is equal to the stress tensor dotted with a unit normal n, and is equal to -pn for the case of negligible viscous stresses.

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