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In summary, if we convert a cylinder into a sphere, the pressure gradient will decrease in proportion to the square of the radius.

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I take it that this shell, whether cylinder or sphere, is of non-negligible thickness and that this thickness is the same for the two situations. I also take it that the pressure difference across the shell is also identical in the two cases.edwardone123 said:

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One would further assume that the diffusion rate through an infinitesimal thickness of shell is in proportion to the pressure gradient across that thickness.

In the case of a cylinder, one can see that to maintain a constant flow rate through all of the concentric shells, the pressure profile across the shell must decrease in proportion to the radius. In the case of a sphere, it must decrease in proportion to the square of the radius.

Have you computed the pressure gradient as a function of radius for the cylindrical situation yet?

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What research have you done so far regarding the fundamentals of (presumably aqueous electrolyte) solution flow and pressure drop through semipermeable membranes?edwardone123 said:

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Not so fast. We're not going to spoon feed this to you. What is the basic equation for the osmotic pressure difference when there is no flow? You are going to have to do some research on your own first before we are willing to help you.edwardone123 said:

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Pressure gradient in a sphere refers to the change in pressure per unit distance within a spherical object. It measures how pressure changes as you move from one point to another within the sphere.

Pressure gradient in a sphere is calculated by dividing the change in pressure by the distance traveled. It is expressed in units of pressure per unit distance, such as Pascals per meter.

The main factors that affect pressure gradient in a sphere are the size of the sphere, the material it is made of, and the internal pressure within the sphere. Other factors may include temperature, external forces, and the presence of any obstacles or irregularities within the sphere.

Pressure gradient in a sphere is an important concept in fluid mechanics and is used to describe the distribution of pressure within a spherical object. It can help predict the behavior of fluids and can be used in various engineering and scientific applications.

Pressure gradient in a sphere is directly related to fluid flow. A steeper pressure gradient indicates a faster flow of fluid, while a flatter pressure gradient indicates a slower flow. This relationship is governed by the laws of fluid dynamics and is crucial in understanding and analyzing fluid systems.

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