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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.

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Chestermiller

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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.

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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?

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?

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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.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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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?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.

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Dale

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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.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?

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.

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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?

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

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Chestermiller

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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: σSaying 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.

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