Daniel Bernoulli (Groningen, 8 February 1700 – Basel, 8 March 1782) was aDutch-Swiss mathematician and was one of the many prominent mathematicians in theBernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability andstatistics. Bernoulli's work is still studied at length by many schools of science throughout the world.
In Physics :-
He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law.[2]
He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation.[9] Bernoulli's principle is of critical use inaerodynamics.[4]
Daniel
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By multiplying with the fluid density ρ, equation (A) can be rewritten as:
or:
where: is dynamic pressure, is the piezometric head or hydraulic head (the sum of the elevation z and the pressure head)[8][9] and is the total pressure (the sum of the static pressure p and dynamic pressure q).[10]
The constant in the Bernoulli equation can be normalised. A common approach is in terms of total head or energy head H:
The above equations suggest there is a flow speed at which pressure is zero, and at even higher speeds the pressure is negative. Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoulli's equation ceases to be valid before zero pressure is reached. In liquids – when the pressure becomes too low – cavitation occurs. The above equations use a linear relationship between flow speed squared and pressure. At higher flow speeds in gases, or for sound waves in liquid, the changes in mass density become significant so that the assumption of constant density is invalid
Simplified form
In many applications of Bernoulli's equation, the change in the ρ g z term along the streamline is so small compared with the other terms it can be ignored. For example, in the case of aircraft in flight, the change in height z along a streamline is so small the ρ g z term can be omitted. This allows the above equation to be presented in the following simplified form:
where p0
Pedro Nune's had many contributions to mathematics but he is best known for his contribution in the national sciences in navigation and cartography. He was the first person to approach it in a mathematical way. He was the person who invented the idea called the loxo drome. he was also the inventor of several measuring devices, called nonius from which the vernier scale was derived.
In conclusion, without the assistance of Poiseuille’s law, a patient with bronchial constriction would not get the adequate amount of oxygen to feed the tissues. Poiseuille’s law states that if the radius of a tube decreases by sixteen percent, the flow rate will decrease by half. In today’s modern medicine
Think about the gas laws we are studying. Boyle’s law tells us that pressure and volume are inversely proportional. Charles’ law states that volume and temperature are directly proportional. We also know that pressure and temperature are directly proportional. Discuss at least one instance in your personal experience where you have seen one or more of these laws in action.
Newton and Boyle's laws have helped to explain how our world and universe works, along with
Blaise Pascal was a brilliant mathematician and experimenter, and he was the voice that still protested against the new science and the materialism of Descartes. His investigations of probability in games of chance produce his very own theorem, and his research in conic sections helped lay the foundations for integral calculus.
The pressure of a gas sample increases for a decrease in volume and decreases for an increase in volume.
Gottfried Wilhelm Leibniz was originally accused of plagiarism of Sir Isaac Newton's unpublished works, but is now regarded as an independent inventor and contributor towards calculus.
Both the orifice and the Venturi meters produce a restriction in the flow and measure the pressure drop across the meter. The velocity of a fluid is expected to increase as the fluid flows from an open area, to a more constricted area. Assuming incompressible flow, a negligible height change, and steady state, Bernoulli’s equation can be simplified to show the correlation between the volumetric flow rate and the pressure drop. The equation for both meters is as follows:
Robert Boyle made many significant contributions to a number of subjects, including chemistry, physics, the discovery of many different unknown properties of air, and making connections between science and his religious beliefs. Many of his discoveries and theories laid the beginning groundwork for a number of the modern sciences used today and added upon previous discoveries from before his time. He greatly impacted the world during the Scientific Revolution time period and his work during that time continues to leave a lasting impression still today. He went up against the accepted beliefs of the time period and disproved many of them in the process of experimentation. In fact, without Robert Boyle, alchemy would still be the main science
Robert Boyle, a philosopher and theologian, studied the properties of gases in the 17th century. He noticed that gases behave similarly to springs; when compressed or expanded, they tend to ‘spring’ back to their original volume. He published his findings in 1662 in a monograph entitled The Spring of the Air and Its Effects. You will make observations similar to those of Robert Boyle and learn about the relationship between the pressure and volume of an ideal gas.
4. The flow velocity increases as the flow gets closer to the barrier wall and reduces as it moves away from the wall. This is because as the flow rate is constant (Conservation of mass) while the area of the flow cross section decreases when it gets closer to the barrier wall, the flow velocity increases. This is best understood by referring to the continuity equation,
This can be represented as : v2 = (elastic property / inertial property). Where the elastic property is usually the bulk modulus or Young's modulus of the medium, and the inertial property is the density of the medium.
The transportation of physiological fluids due to continuous wavelike muscle contraction and relaxation of physiological vessels is known as peristalsis. In many physiological situations, peristalsis is used by the body to propel or mix the contents of a tube, for example, in a ureter, gastrointestinal tract, the bile duct and the other glandular ducts. One of the importances of using peristaltic pumping is avoiding use any internal moving parts such as pistons, in the pumping process. The peristaltic motion in the fluid mechanics is the dynamic interaction of flexible boundary with the fluid. A large amount of information on the topic existed after the work initiated by Latham [1] and Shapiro et al. [2] via theoretical and experimental approaches.
Considering a viscous liquid that is being pumped through a smooth pipe with the parameters:
He proposed that under certain circumstances light could be considered a particles. He also hypothesized that the energy carried by a photon is depositional to the frequency of radiation. The formula E= HU proves this. Virtually no one accepted this theory but thought differently when Robert Andrews Millikan proved it.