By measuring the difference in fluid pressure between the normal pipe section and at the vena contracta, the volumetric and mass flow rates can be obtained from Bernoulli's equation.

By assuming steady-state, incompressible ( constant fluid density ), inviscid, laminar flow in a horizontal pipe ( no change in elevation ) with negligible frictional losses, Bernoulli's equation reduces to an equation relating the conservation of energy between two points on the same streamline:

By applying this general principle, a great number of complex compounds of osmium, ruthenium, iridium, and rhenium, with triphenylphosphine, triphenylarsine, and triphenylstibine have been obtained in this laboratory during the past few years.

By the well ordering principle, if there are positive integers that satisfy a given property, then there is a smallest positive integer that satisfies that property ; therefore, there is a smallest positive integer satisfying the property " not definable in under eleven words ".

By the same principle when the pH is too high, the kidneys excrete bicarbonate ( HCO < sub > 3 </ sub >< sup >-</ sup >) into urine as urea via the Urea Cycle ( aka the Krebs-Henseleit Ornithine Cycle ).

By the mid-19th century, however, the powerful British Empire gave up mercantilism and trade restrictions and introduced the principle of free trade, with few restrictions or tariffs.

By voluntarily stepping down and disbanding his army when the war was won, he permanently established the principle of civilian supremacy in military affairs.

By the superposition principle, the wavepacket at any time t is:

By applying the variational principle to the action

By the same principle, 10 is the least common multiple of-5 and 2 as well.

By principle, originalists are generally unwilling to defer to precedent when precedent seems to come into conflict with the Constitution.

It is for them alone to point out what we ought to do … By the principle of utility is meant that principle which approves or disapproves of every action whatsoever according to the tendency it appears to have to augment or diminish the happiness of the party whose interest is in question: or, what is the same thing in other words to promote or to oppose that happiness.

By this I mean the principle that, in deciding what is good and what is bad for a given individual, the ultimate criterion can only be his own wants and his own preferences .”

By 1865, the German physicist Rudolf Clausius had shown that this equivalence principle needed amendment.

By the principle of mathematical induction it follows that the result is true for all natural numbers.

By analyzing the bank accounts of certain members of the ring, he obtained legal proof of the principle on which the spoils had been divided.

By then the mujtahid would be able to issue his own edicts from the sources of Islamic religious laws: the Qur ' an, the Sunnah, ijmāʻ, and ' aql (" intellect ", rather than the Sunnī principle of qiyas ).

By principle, half of the inhabitants are Jewish Israelis, the rest are Muslim and Christian Arabs.

By weighting utility variations by the marginal utilities, the social welfare function implicit to the Kaldor – Hicks compensation principle is represented by anti-egalitarian, concave indifference curves.

By the equivalence principle gravitational stress-energy will always vanish locally at any chosen point in some chosen frame, therefore gravitational stress-energy cannot be expressed as a non-zero tensor ; instead we have to use a pseudotensor.

By the pigeonhole principle, the probability reaches 100 % when the number of people reaches 367 ( since there are 366 possible birthdays, including February 29th ).

By the Leonid Brezhnev period democratic centralism was described, in the 1977 Soviet Constitution, as a principle for organizing the state: " The Soviet state is organized and functions on the principle of democratic centralism, namely the electiveness of all bodies of state authority from the lowest to the highest, their accountability to the people, and the obligation of lower bodies to observe the decisions of higher ones.

By stressing prosopographical analysis, Syme rejected the force of ideas in politics, dismissing most such invocations of constitutional and political principle as nothing more than " political catchwords.

By examining " hotter " and " cooler " spark plugs of the same manufacturer side by side, the principle involved can be very clearly seen ; the cooler plugs have a more substantial ceramic insulator filling the gap between the center electrode and the shell, effectively allowing more heat to be carried off by the shell, while the hotter plugs have less ceramic material, so that the tip is more isolated from the body of the plug and retains heat better.

" Musicologist Jean-Jacques Nattiez summarizes the relativist, post-modern viewpoint: " The border between music and noise is always culturally defined — which implies that, even within a single society, this border does not always pass through the same place ; in short, there is rarely a consensus ... By all accounts there is no single and intercultural universal concept defining what music might be.

By the two-seed theory, the embryo is not conceived unless the male and female seed meet: this implies a bilineal, or cognatic, theory of relationship.

By Newton's first law, this situation implies that the net force and net torque ( also known as moment of force ) on every part of the system is zero.

" By this Zelman implies that Utopia influenced Vladimir Lenin's Bolsheviks, despite their brutal repression of organised religion.

By asserting that biological factors are the primary determinants of behaviour, biological determinism implies of course that non-biological factors, such as social customs, expectations and education, have less or no effect on behaviour.

In the following excerpt, from William Shakespeare's Romeo and Juliet, Romeo, in saying " all combined, save what thou must combine By holy marriage " implies that it is not marriage with Juliet that he seeks but simply to be joined with her romantically.

By exactly the same reasoning as in the translational case, equipartition implies that in thermal equilibrium the average rotational energy of each particle is ( 3 / 2 ) k < sub > B </ sub > T.

By the connectedness result this implies it is irreducible if ρ > 0.

By the Riesz representation theorem, this implies that for every x in X there exists a unique element K < sub > x </ sub > of H with the property that:

This implies that there is a well-defined norm-one linear form on the subspace Ru + Y taking tu + y to t. By the Hahn – Banach theorem the latter admits a norm-one linear extension on ℓ < sup >∞</ sup >( Z ), which is by construction a shift-invariant finitely additive probability measure on Z.

By induction, the hypothesis implies that M < sup > k </ sup > T

By the time the Retriangulation was completed electronic distance-measuring devices had come into use which could have greatly reduced the overall error ( it now seems Great Britain is 20 + metres shorter than OSGB36 implies ) but starting over from scratch was presumably out of the question.

By way of an analogy, the argument states that design implies a designer.

By considering other games, we can show that Π < sup > 1 </ sup >< sub > n </ sub > determinacy implies that every Σ < sup > 1 </ sup >< sub > n + 1 </ sub > set of reals has the property of Baire, is Lebesgue measurable ( in fact universally measurable ) and has the perfect set property.

By definition, strain implies discomfiture, so it should follow that molecules with large amounts of transannular strain should have higher energies than those without.

By this method it was determined that the normal pressure exerted by a sample of polybutene ( molecular weight reported to be 770 ) was over half an atmosphere.

By the very nature of the situation, it is the union which has been able to select the time and place to bring pressure upon management.

By controlling the pressure and temperature applied to phenol and formaldehyde, he produced a hard moldable material and patented in 1907 known as Bakelite.

By 30 July the Greek army was outnumbered by the counter-attacking Bulgarian army, which attempted to encircle the Greeks in a Cannae-type battle, by applying pressure on their flanks.

By regulating the processing parameters — especially the gases introduced, but also including the pressure the system is operated under, the temperature of the diamond, and the method of generating plasma — many different materials that can be considered diamond can be made.

By the 1870s, British physicist William Crookes and others were able to evacuate tubes to a lower pressure, below 10 < sup >− 6 </ sup > atm.

By 1908 public and diplomatic pressure led Leopold II to the annex the Congo as the Belgian Congo colony.

By Raoult's law, some of the target compound will vaporize ( in accordance with its partial pressure ).

By exposing an azeotrope to a vacuum or positive pressure, it's possible to bias the boiling point of one component away from the other by exploiting the differing vapour pressure curves of each ; the curves may overlap at the azeotropic point, but are unlikely to be remain identical further along the pressure axis either side of the azeotropic point.

At standard temperature, pressure and concentration conditions, the cell's emf ( measured by a multimeter ) is 0. 34 V. By definition, the electrode potential for the SHE is zero.

By varying the air pressure, a flute player can also change the pitch of a note by causing the air in the flute to resonate at a harmonic other than the fundamental frequency without opening or closing any holes.

By contrast, the continental high pressure system situated over the Eurasian continent counteracts the maritime influences, occasionally causing severe winters and high temperatures in the summer.

By increasing the concentration of oxygen in the air, the effects of lower barometric pressure are countered and the level of arterial pO < sub > 2 </ sub > is restored toward normal capacity.

By 2000, the consolidation of grocery store chains, the spread of retailers like Wal-Mart, and growth of private-label brands caused competition for shelf space, and put price pressure on the company's products.

By 25 May 1993, the international community had tried to pressure the leaders of the former Yugoslavian republics diplomatically, militarily, politically, economically, and – with Resolution 827 – through juridical means.

By using the streamwise vector i parallel to the freestream in place of k in the integral, we obtain an expression for the pressure drag D < sub > p </ sub > ( which includes induced drag in a 3D wing ).

By 1944 US and British air forces were sending huge air fleets over occupied Europe, increasing the pressure on the Luftwaffe day and night fighter forces.

“ By allowing deals with Burma ’ s state-owned oil company, the U. S. looks like it caved to industry pressure and undercut Aung San Suu Kyi and others in Burma who are promoting government accountability ,” HRW ’ s Business and Human Rights Director Arvind Ganesan said.

By comparison, the atmospheric pressure at the summit of Mount Everest is 32, 000 pascals, or about 32 % of Earth's sea level pressure.

By overblowing, that is, increasing the pressure of breath and tension of lips, odd harmonics ( notes whose frequencies are odd-number multiples of the fundamental ), near a 12th in cylindrical tubes, may also be produced.

By using pressure politics on legislators, the Anti-Saloon League achieved the goal of nationwide prohibition during World War I, emphasizing the need to destroy the political corruption of the saloons, the political power of the German-based brewing industry, and the need to reduce domestic violence in the home.