Is pressure directly proportional to area in fluids and speed of liquid increase and its pressure decrease when a liquid passes through the construction in a horizontal pipe?
The statement that pressure is directly proportional to area in fluids is incorrect. In fact, the opposite is true: pressure is inversely proportional to area in fluids. This means that as the area increases, the pressure decreases, and vice versa.
Here's why:
- Pressure is defined as the force exerted per unit area. Imagine a piston pushing down on a container of fluid. The same force applied to a larger piston (larger area) will result in a lower pressure compared to using a smaller piston (smaller area). This is because the force is distributed over a larger surface area.
Now, regarding your second question:
- Liquid speed and pressure are related through Bernoulli's principle, which states that in a steady, incompressible flow, an increase in the speed of the fluid is accompanied by a decrease in its pressure. This applies to liquids flowing through constrictions in horizontal pipes.
When a liquid encounters a constriction (narrowing) in a horizontal pipe, its speed increases due to the limited space. According to Bernoulli's principle, this increase in speed leads to a decrease in pressure in the constricted region.
So, to summarize:
- Pressure is inversely proportional to area in fluids.
- Liquid speed increases and pressure decreases when the liquid passes through a constriction in a horizontal pipe due to Bernoulli's principle.
In fluid mechanics according to continuity equation A1 X V1 =A2 X V2 , showing velocity inversely proportional to cross sectional area , since in FM it is well known that velocity is inversely proportional to pressure, this inverse relation of velocity with area and pressure gives direct relation. As area decreases velocity increases and pressure at that point decreases. But we also know that pressure is inversely proportional to area[P=F/A]. The higher the velocity of a fluid (liquid or gas), the lower the pressure it exerts. This is called Bernoulli's Principle. Fluid pressure is caused by the random motion of the fluid molecules. Pressure equals force divided by area ( P = F A ). The equation shows that pressure is directly proportional to force, but inversely proportional to area. At a constant area, pressure increases as the magnitude of the force applied also increases. Similarly, in fluid flow, when the fluid speeds up (increases its velocity), it has less energy to exert as pressure. So, as the speed of the fluid goes up, the pressure it can exert goes down, and vice versa. As per equation of continuity, when the liquid flows through a constriction, the area of cross-section of the liquid decreases, therefore the velocity of the liquid increases. Thus, as the fluid passes through the constriction or throat, the higher speed results in lower pressure at the throat.
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