In
1738,
physicist and
mathematician Daniel Bernoulli published
Hydrodynamica, a work that contained the
first correct analysis of
water flowing from a
hole in a container. This book considered the
basic properties of
fluid flow,
pressure,
density and
velocity and gave their
fundamental relationship through what is now known as
Bernoulli's principle.
Bernoulli's principle essentially states that:
p + (½ * P * v^2) + (P * g * h) = constant
Where: p= pressure; P= density; v= velocity; h= elevation; g= gravitational acceleration
Provided that:
-Points 1 and 2 are on a streamline
-The fluid has constant density
-The flow is steady
-There is no friction
When a fluid moves, the pressure within the fluid is no longer only due to all of the weight above it. Instead, the fluid will begin to loose pressure according to Bernoulli's equation.
By relating Bernoulli's equation to the Continuity Equation you can prove this. It is known that when a fluid is in motion, it must move in such a way that mass is conserved. To see how mass conservation
places restrictions on the velocity field consider the steady flow of fluid through an opening. The inflow and outflow are one-dimensional, so the velocity and density are constantover the area A.
Taking this into consideration, it can also be proven that:
-decreasing area = increasing velocity
-increasing velocity = decreasingpressure
These facts make the principle more variant because the rate that the water comes out is dependent on how much water is above the hole pressing down, and as this water drains the amount decreases and so the pressure decreases. Thus, the rate of drainage is exponential – the less water in the container the faster it will drain out.
The practical applications of Bernoulli's principle are far reaching. Bernoulli himself discovered one before he had even created the proper equation for it. Bernoulli discovered the first way to accurately measure blood pressure. He wanted to find a relationship between the speed at which blood flows and it's pressure. He experimented by puncturing the wall of a pipe with a small, open-ended straw and noted that the height that the fluid rose up the straw was related to the fluid's pressure in the pipe. Soon physicians all over Europe were measuring their patient's blood pressure by sticking point-ended glass tubes directly into their arteries.
Luckily, 170 years later another man discovered the less painful method still in use today. (The one they wrap around your arm.) Nevertheless, Bernoulli's original method of measuring pressure is still used today in other areas, such as to measure the air speed of an aircraft.