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
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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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