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Pressure of Fluids

Pressure of Fluids

There are many examples of pressure in fluids in everyday life, such as in relation to blood (high or low blood pressure) and in relation to weather (high- and low-pressure weather systems). A given force can have a significantly different effect, depending on the area over which the force is exerted. For instance, a force applied to an area of 1 mm2 has a pressure that is 100 times greater than the same force applied to an area of 1 cm2. That's why a sharp needle is able to poke through skin...

Pressure Variation in a Fluid at Rest

Pressure Variation in a Fluid at Rest

In a fluid at rest, the pressure at any point beneath the fluid surface depends solely on the depth, not on the container's shape or size. This principle, known as hydrostatic pressure, arises because, in stationary fluids, there is no acceleration, meaning the forces within the fluid balance out. Only vertical forces, caused by the weight of the fluid above, contribute to pressure changes with depth.
When measuring pressure at two different levels within the fluid, the difference in pressure...

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:

Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...

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Related Experiment Video

Updated: Jul 8, 2026

Ultrasound Based Assessment of Coronary Artery Flow and Coronary Flow Reserve Using the Pressure Overload Model in Mice

Ultrasound Based Assessment of Coronary Artery Flow and Coronary Flow Reserve Using the Pressure Overload Model in Mice

Published on: April 13, 2015

The high zero-flow pressure phenomenon in coronary circulation: a simulation study.

Tahseen Ejaz¹, Tadashi Takemae, Yukio Kosugi

¹Venture Business Laboratory, Shizuoka University Faculty of Engineering, 3-5-1 Johoku, Hamamatsu 432-8561, Japan. ejaz@mail.vbl.shizuoka.ac.jp

Frontiers of Medical and Biological Engineering : the International Journal of the Japan Society of Medical Electronics and Biological Engineering

|May 9, 2003

Summary

This study used a dynamic simulation of coronary vessels to investigate high zero-flow pressure. Researchers found a nearly linear relationship between diastolic arterial pressure and diastolic arterial flow, with a zero-flow intercept around 40 mmHg.

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Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery

Intravascular Ultrasound Image-Based Finite Element Modeling Approach for Quantifying In Vivo Mechanical Properties of Human Coronary Artery

Published on: December 6, 2024

Area of Science:

Cardiovascular physiology
Biomedical engineering
Computational fluid dynamics

Background:

The zero-flow pressure phenomenon in coronary circulation is not fully understood.
Accurate modeling of coronary hemodynamics is crucial for understanding cardiovascular diseases.

Purpose of the Study:

To investigate the high zero-flow pressure phenomenon in coronary circulation.
To establish the relationship between diastolic arterial pressure and diastolic arterial flow using a dynamic simulation.
To determine the zero-flow pressure intercept in the coronary system.

Main Methods:

Developed an electronic model of the coronary vessel.
Performed a dynamic simulation to analyze hemodynamic parameters.
Focused on diastolic phases to assess pressure-flow relationships.

Main Results:

The relationship between diastolic arterial pressure and diastolic arterial flow was found to be approximately linear.
A zero-flow pressure intercept of approximately 40 mmHg was identified.
Simulation results align with existing animal experimentation data.

Conclusions:

The dynamic simulation provides a valuable tool for studying coronary hemodynamics.
The identified linear relationship and pressure intercept offer insights into coronary physiological regulation.
Findings support the validity of the electronic model in replicating in-vivo phenomena.