# International System Units

#### Alfa_ET

Joined Feb 26, 2011
17
What is the partial derivative of pressure (bar) with respect to time?

is it m^3/s?

#### t_n_k

Joined Mar 6, 2009
5,455
If 1 bar = 100kPa where the Pascal [Pa] is the SI unit of pressure then presumably the unit for the time derivative (rate of change) of pressure is $$P_as^{-1}$$

$$1 \ P_a=1 \ kgm^{-1}s^{-2}$$

So presumably the unit of the time derivative of pressure in terms of the fundamental units is

$$kgm^{-1}s^{-3}$$

#### Georacer

Joined Nov 25, 2009
5,182
Actually, I think it is $$\frac{\partial P(bar)}{\partial t}=100k \cdot (-2) kgm^{-1}s^{-3}$$
given that the formula for the pressure is as you say.

#### t_n_k

Joined Mar 6, 2009
5,455
If the question was actually about conversion between units then perhaps more succinctly

$$1 \ Bars^{-1} \ <=> \ 100 \ kPas^{-1} \ <=> \ 10^5 \ kgm^{-1}s^{-3}$$

I doubt the OP has any real ongoing interest in this matter.

#### Georacer

Joined Nov 25, 2009
5,182
But the partial derivative of a function in respect to the time is
$$\frac{df}{dt}$$
not
$$\frac{f}{s}$$

One of us has a really brain-dead moment. By the end of the thread we 'll see who it is. (Please let it not be me!)
Now I saw the units reference. It was me who had the brain dead moment after all. Sigh...