pascal

Examples of pascal in the following topics:

• Pascal's Principle

  • Pascal's Principle states that pressure is transmitted and undiminished in a closed static fluid.
  • Pascal's Principle (or Pascal's Law) applies to static fluids and takes advantage of the height dependency of pressure in static fluids.
  • Named after French mathematician Blaise Pascal, who established this important relationship, Pascal's Principle can be used to exploit pressure of a static liquid as a measure of energy per unit volume to perform work in applications such as hydraulic presses.
  • Quantitatively, Pascal's Law is derived from the expression for determining the pressure at a given height (or depth) within a fluid and is defined by Pascal's Principle:
  • By Pascal's Principle, P1 = P2, yielding a force exerted by the static fluid of F2, where F2 > F1.

• Binomial Expansions and Pascal's Triangle

  • The binomial theorem, which uses Pascal's triangles to determine coefficients, describes the algebraic expansion of powers of a binomial.
  • The rows of Pascal's triangle are numbered, starting with row $n = 0$ at the top.
  • Notice the coefficients are the numbers in row two of Pascal's triangle: 1, 2, 1.
  • where the coefficients $a_i$ in this expansion are precisely the numbers on row $n$ of Pascal's triangle.
  • Notice that $n=5$, and recall that this would correspond to row 5 of Pascal's triangle.

• High Pressure

  • The technique was named after Blaise Pascal, whose work included detailing the effects of pressure on fluids.
  • Although commercial products preserved by pascalization first emerged in 1990, the technology behind pascalization is still being perfected for widespread use.
  • In pascalization, food products are sealed and placed into a steel compartment containing a liquid, often water, and pumps are used to create pressure.
  • During pascalization, more than 50,000 pounds per square inch (340 MPa) may be applied for around fifteen minutes, leading to the inactivation of yeast, mold, and bacteria.
  • Because pascalization is not heat-based, covalent bonds are not affected, causing no change in the food's taste.

• SI Units of Pressure

  • The SI unit of pressure is the pascal (Pa), which is equal to one Newton per meter squared (N/m2).
  • The unit of pressure in the SI system is the pascal (Pa), defined as the force of one newton per square meter:
  • What is the pressure in pascals?

• Total Number of Subsets

  • The binomial coefficients appear as the entries of Pascal's triangle where each entry is the sum of the two above it.
  • These coefficients for varying $n$ and $b$ can be arranged to form Pascal's triangle.

• Finding a Specific Term

  • You might multiply each binomial out to identify the coefficients, or you might use Pascal's triangle.
  • The coefficients of the first and last terms are both 1 and they follow Pascal's triangle.

• The Development of Social Science

  • For examples see Blaise Pascal, Gottfried Leibniz and Johannes Kepler, each of whom took mathematical examples as models for human behavior directly.
  • In Pascal's case, the famous wager; for Leibniz, the invention of binary computation; and for Kepler, the intervention of angels to guide the planets.

• Pressure

  • In SI units, the unit of pressure is the Pascal (Pa), which is equal to a Newton / meter2 (N/m2).

• Spin-Spin Splitting

  • The intensity ratio of these lines is given by the numbers in Pascal's triangle.
  • To see how the numbers in Pascal's triangle are related to the Fibonacci series (3rd diagram below).

• Physics and Engineering: Fluid Pressure and Force

  • While pressure may be measured in any unit of force divided by any unit of area, the SI unit of pressure (the newton per square meter) is called the pascal (Pa).