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## Main Question or Discussion Point

Sorry if the formulation is imprecise, I'm a biology major trying to study some physics. The question is:

Thanks for any clarification!

So far, my reasoning is:569. When comparing two points of fluid flowing through the same horizontal pipe, if the fluid velocity is greater, then

A. the temperature is less

B. the temperature is greater

C. the temperature is unchanged

D. the pressure is greater

I make an assumption in Step (2) that decreasing the pressure will decrease the temperature. But I'm not sure what the justification is. I only know of the ideal gas law, and I'm not sure if the behavior is the same for incompressible fluids. Maybe incompressibility means fluid is similar to ideal gas behavior, or maybe it holds in general and the incompressibility assumption can be removed? Or maybe it's dependent on the fluid?From Bernoulli's equation, you have

(1/2)(\rho)v^2 + \rho*g*h + P = constant

where \rho = density, v = velocity, g = acceleration due to gravity, h = height and P = pressure.

If the first term increases, one or both of the other two terms must decrease in order to satisfy the relationship. How can this happen?

(1) \rho*g*h decreases. This means either \rho, g, or h decreases. Since the fluid is incompressible (assumption I'm making), \rho is constant and cannot decrease. g is a constant and cannot decrease. So it's possible that the height decreased. But that's not one of the answer choices.

(Note: If the fluid were not incompressible, a possible answer would be that \rho, the density, decreases. Since volume is constant, this would mean the mass of the fluid decreased. This is not an answer choice.)

(2) P decreases. Notice that the question says "same horizontal pipe", which means the volume doesn't change to compensate. So the pressure in a fixed volume is being decreased, which means it can be reasonably be assumed (too lazy to go through the math of the relationship between pressure/volume and temperature for fluids, I'm assuming it's similar to gases) that the temperature decreases. That's why I would say it's A.

Thanks for any clarification!