Question

use dimensional analysis to check if the expression P=(yv^2)/2 + ygh is correct. Given that P is pressure in pascal, y is density in kgm^-3 , v is velocity in m/s, g is acceleration due to gravity in m/s^2 and h is the height in m(metre).​

Answer 1

Answer: The expression is correct

Step-by-step explanation:

We have the following expression:

`P=(yv^(2))/(2) + ygh`

Where:

Pressure:
`P` in units of Pascal (
`Pa`)

`1 Pa= 1 (N)/(m) = (kg m/s^(2))/(m)=(kg)/(ms^(2))`

Density:
`y` in units of
`(kg)/(m^(3))`

Velocity:
`v` in units of
`(m)/(s)`

Acceleration due to gravity:
`g` in units of
`(m)/(s^(2))`

Height:
`h` in units of
`m`

Knowing this, let's begin with the dimensional analysis:

`Pa=\frac{((kg)/(m^(3))){((m)/(s))}^(2)}{2} + ((kg)/(m^(3)))((m)/(s^(2)))(m)`

`Pa=((kg)/(ms^(2)))/(2) + (kg)/(ms^(2))`

`Pa=(1)/(2) (kg)/(ms^(2)) + (kg)/(ms^(2))`

Remembering
`1 Pa=(kg)/(ms^(2))`, we are able to know this expression is correct.