Answer: The expression is correct
Explanation:
We have the following expression:
[tex]P=\frac{yv^{2}}{2} + ygh[/tex]
Where:
Pressure: [tex]P[/tex] in units of Pascal ([tex]Pa[/tex])
[tex]1 Pa= 1 \frac{N}{m} = \frac{kg m/s^{2}}{m}=\frac{kg}{ms^{2}}[/tex]
Density: [tex]y[/tex] in units of [tex]\frac{kg}{m^{3}}[/tex]
Velocity: [tex]v[/tex] in units of [tex]\frac{m}{s}[/tex]
Acceleration due to gravity: [tex]g[/tex] in units of [tex]\frac{m}{s^{2}}[/tex]
Height: [tex]h[/tex] in units of [tex]m[/tex]
Knowing this, let's begin with the dimensional analysis:
[tex]Pa=\frac{(\frac{kg}{m^{3}}){(\frac{m}{s})}^{2}}{2} + (\frac{kg}{m^{3}})(\frac{m}{s^{2}})(m)[/tex]
[tex]Pa=\frac{\frac{kg}{ms^{2}}}{2} + \frac{kg}{ms^{2}}[/tex]
[tex]Pa=\frac{1}{2} \frac{kg}{ms^{2}} + \frac{kg}{ms^{2}}[/tex]
Remembering [tex]1 Pa=\frac{kg}{ms^{2}}[/tex], we are able to know this expression is correct.
