Stress Strain Curve

Step 1: Application of Bernoulli's principle.
Bernoulli's principle states that for an incompressible fluid in streamline flow, the total mechanical energy (pressure energy, kinetic energy, and potential energy) remains constant. Mathematically: where is pressure, is fluid density, is velocity, and is height.

Step 2: At the narrowest part of the pipe.
In a horizontal pipe: At the narrowest part of the pipe, velocity ( ) is maximum due to the conservation of mass ( ). As velocity increases, pressure decreases to maintain the constant total energy.

Step 1: Understanding Bernoulli's principle.
Bernoulli's principle states that for an incompressible, non-viscous fluid in streamline flow: where: : Pressure of the fluid, : Density of the fluid, : Velocity of the fluid, : Height of the fluid.

Step 2: Application to a horizontal pipe.
For a horizontal pipe ( is constant), the equation simplifies to: This implies that when the velocity ( ) of the fluid increases, the pressure ( ) decreases, and vice versa.

Step 3: Narrowest part of the pipe.
At the narrowest part of the pipe: The cross-sectional area is minimum. By the equation of continuity ( ), the velocity is maximum. By Bernoulli's principle, the pressure is minimum.

Step 4: Conclusion.
At the narrowest part of the pipe, the velocity is maximum, and the pressure is minimum.