2.9. Pressure Forces

Now, the question is, what are the forces acting on fluid in the control volume? So, one is gravity, other is shear at solid surface or pressure at solid surface, pressure on the flow surfaces.

In this chunk, we introduce the different types of forces acting on fluids within a control volume. The main forces are gravitational force that pulls the fluid downwards, shear forces that act at the surfaces of solids in contact with the fluid, and pressure forces exerted by the fluid itself on the surface it flows against. Understanding these forces is crucial for analyzing fluid behavior in various engineering applications.

Consider when you hold a garden hose to water flowers. The weight of water in the hose represents gravitational force, while the grip on the hose represents shear forces resisting the flow of water. The pressure pushing the water out of the end of the hose comes from the force of water moving through the hose. Like in this example, pressure forces and gravitational effects work together in all fluid systems.

So, we can simply write F = W + F p1 + F p2 + F ss, and ma force, mass into acceleration is M 1 + M 2.

This formula explains how we calculate the net force acting on the fluid. F represents the total net force, which includes the weight (W) of the fluid acting downwards, pressure forces (F p1 and F p2) acting at the inlet and outlet of the control volume, and shear forces (F ss) acting at the surfaces in contact with the fluid. On the other side of the equation, we have the mass times acceleration, which gives us M1 + M2, where M1 and M2 are the masses associated with fluid entering and leaving the control volume. The balance between these forces and mass changes is essential in fluid mechanics to ensure steady fluid flow.

Imagine pushing a spaghetti noodle through boiling water. Here, the weight of the water and the pressure from boiling bubbles represent the forces acting against your push. The moment you stop pushing, the net force acting on the noodle settles to zero as all forces balance out without any movement.

So, we can simply write M 1 + M 2 = W + F p1 + F p2 + F ss, and M 1 here is - ρ Q V 1 and M 2 is ρ Q V 2.

Here, we break down the terms of the equation further. M1 and M2 are the momentum changes of the fluid at two different points; they detail how the density (ρ), flow rate (Q), and velocities (V1, V2) interact to describe changes in motion. The negative and positive sign convention plays a role here; the mass flowing into the control volume and leaving contributes to either positive or negative momentum. Understanding these individual components helps us analyze how pressure forces can change when the flow conditions vary.

Think of a water slide. As a child descends, their weight (W) represents the gravitational pull. The water flowing (Q) acts on them, and the pressures they feel when going down can represent Fp1 and Fp2, where they 'push' and 'squeeze' against the channel walls. Each element of the slide contributes pressure, affecting the child's speed and experience.

Now, pipe wants to move up that is why this the net force is in the downward direction.

In this concluding part, we summarize that the calculations of forces lead us to determine how the system behaves under pressure and weight forces. If the net force indicates a downward direction, it shows that the cumulative effects from pressures (positive) and the opposing weight (negative) lead the pipe to want to move up or down. This understanding is fundamental in predicting and controlling fluid dynamics, especially in engineering applications like pipe systems and fluid-gathering structures.

Consider a submarine submerged underwater. The pressure from the water surrounds it, while buoyancy wants to lift it towards the surface; this balance controls its depth. If the net force calculation indicates strong sinking pressure outweighs buoyancy, the submarine descends lower. Understanding these forces in practice ensures safety and operational effectiveness in real-world marine engineering.

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