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A useful theoretical equation for computing the relation between pressure, velocity, and altitude in a steady flow of a nearly inviscid, nearly incompressible fluid with negligible heat transfer and shaft work is the Bernoulli relation, named after Daniel Bernoulli, who published a hydrodynamics textbook in 1738: Po = p + ipV² + pgZ (1) where po = stagnation pressure p = pressure in moving fluid V = velocity p = density Z = altitude gravitational acceleration (a) Show that Eq. (1) satisfies the principle of dimensional homogeneity, which states that all additive terms in a physical equation must have the same dimensions. (b) Show that consistent units result without additional conversion factors in SI units. (c) Repeat (b) for BG units.

A useful theoretical equation for computing the relation between pressure, velocity, and altitude in a steady flow of a nearly inviscid, nearly incompressible fluid with negligible heat transfer and shaft work is the Bernoulli relation, named after Daniel Bernoulli, who published a hydrodynamics textbook in 1738: Po = p + ipV² + pgZ (1) where po = stagnation pressure p = pressure in moving fluid V = velocity p = density Z = altitude gravitational acceleration (a) Show that Eq. (1) satisfies the principle of dimensional homogeneity, which states that all additive terms in a physical equation must have the same dimensions. (b) Show that consistent units result without additional conversion factors in SI units. (c) Repeat (b) for BG units.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A useful theoretical equation for computing the relation between pressure, velocity, and altitude in a steady flow of a nearly inviscid, nearly incompressible fluid with negligible heat transfer and shaft work is the Bernoulli relation, named after Daniel Bernoulli, who published a hydrodynamics textbook in 1738: Po = p + ipV² + pgZ (1) where po = stagnation pressure p = pressure in moving fluid V = velocity p = density Z = altitude gravitational acceleration (a) Show that Eq. (1) satisfies the principle of dimensional homogeneity, which states that all additive terms in a physical equation must have the same dimensions. (b) Show that consistent units result without additional conversion factors in SI units. (c) Repeat (b) for BG units.
Transcribed Image Text:A useful theoretical equation for computing the relation between pressure, velocity, and altitude in a steady flow of a nearly inviscid, nearly incompressible fluid with negligible heat transfer and shaft work is the Bernoulli relation, named after Daniel Bernoulli, who published a hydrodynamics textbook in 1738: Po = p + ipV² + pgZ (1) where po = stagnation pressure p = pressure in moving fluid V = velocity p = density Z = altitude gravitational acceleration (a) Show that Eq. (1) satisfies the principle of dimensional homogeneity, which states that all additive terms in a physical equation must have the same dimensions. (b) Show that consistent units result without additional conversion factors in SI units. (c) Repeat (b) for BG units.
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