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Consider the following diagram. All textbooks I read don't explain why the forces are assumed to be inward. Could you tell me the reason?

enter image description here

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  • $\begingroup$ It's just a guess, but I've been doing some reading on thermodynamics lately, and was surprised to find that passage thru time, irreversible on the macroscale, is locally reversible on the microscale, which the upper part of your diagram would be approximating more closely. $\endgroup$
    – Edouard
    Jun 13, 2021 at 21:04
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    $\begingroup$ Pressure acts normal to the surfaces of the control volume body of fluid, and, when we do a force balance on a body, we include only the forces that the exterior bodies exert of the body under consideration, not the forces that the body exerts on the exterior bodies. Which direction do you think the exterior pressures are acting on the body of fluid? $\endgroup$ Jun 14, 2021 at 11:34
  • $\begingroup$ @ChetMiller: The exterior agent cannot pull the body under consideration? $\endgroup$ Jun 14, 2021 at 12:14
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    $\begingroup$ Not within the framework of the usual Bernoulli equation development in which viscous and viscoelastic tensile stresses are considered negligible. $\endgroup$ Jun 14, 2021 at 13:00
  • $\begingroup$ @ChetMiller: Thank you very much! $\endgroup$ Jun 14, 2021 at 13:12

2 Answers 2

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Pressure acts normal to the surfaces of the control volume body of fluid, and, when we do a force balance on a body, we include only the forces that the exterior bodies exert of the body under consideration, not the forces that the body exerts on the exterior bodies. The external pressure force F2 acts in the direction indicated in the figure.

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In the case that the pressure is positive (which it usually is) the inward-pointing arrows correctly indicate the direction of force exerted on the fluid in the pictured tube by the fluid outside the tube.

You could draw the arrows outwards if you replace $p_1$, $p_2$ in the expressions $p_1A_1$ and $p_2A_2$ by $-p_1$ and $-p_2$.

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