Bernoulli's Equations

The relationship between the speed and pressure of flowing (Inids is given by Bernoulli's equation. It governs why planes lly, how blood flows through our bodies and how fuel is injected into car engines. Fast flowing fluids create low pressure that explains the lift associated with an aircraft wing and I he narrowing of a jet of water coming from a tap. Using ihis effect to measure blood pressure, Daniel Bernoulli himself inserted tubes directly into his patients9 veins. When you run a tap, the column of water that flows from it is narrower than the aperture of the tap itself. Why is this? And how is this related to how planes fly and angioplasties?

Dutch physicist and medical doctor Daniel Bernoulli understood that moving water creates low pressure. The faster it flows, the lower its pressure. If you imagine a clear glass tube lying horizontally with water pumped through it, you can measure the pressure of that water by inserting a clear capillary tube vertically into the first pipe and watching how the height of water in the smaller tube changes. If the pressure of the water is high, the water level in the capillary rises. If it is low it drops.

When Bernoulli increased the speed of the water in the horizontal tube he observed a drop in pressure in the vertical capillary tube - this pressure drop proved proportional to the velocity of the water squared. So any flowing water, or fluid, has a lower pressure than still water. Water flowing from a tap has low pressure compared to the still air around it and so it is sucked into a narrower column. This applies to any fluid, from water to air.

Blood flow Trained in medicine, Bernoulli himself was fascinated by the flow of blood though the human body and invented a tool to be able to measure blood pressure. A capillary tube, inserted into a blood vessel, was used for nearly two hundred years to measure blood pressure in live patients. It must have been a relief for all concerned to find a less invasive method. Just like water in a pipe, blood in an artery is pumped away from the heart along a pressure gradient that is set up along the length of the vessel. If an artery is narrowed, then the speed of blood flowing through the constriction increases according to Bernoulli's equation. If the vessel is half as narrow, then the blood that flows through it is four times faster (two squared). This quickening of blood flow through restricted arteries can cause problems. First, the flow may become turbulent, if its speed is fast enough, and eddies may be produced. Turbulence near the heart produces heart murmurs with a characteristic sound that doctors can recognize. Also, the pressure drop in the constricted area may suck in the soft artery wall, further aggravating the problem. If the artery is expanded, with an angioplasty, the volume of flow will increase again and all will be well.