Flight instruments can be modeled with simple formulas. I find this to be a helpful aid to thinking through failure modes.
## Definitions
* $P_p(t)$: Pressure measured at pitot tube at moment $t$
* $P_s(t)$: Pressure measured at static port at moment $t$
* $A$: Altimeter setting
* $VSI(t)$: display on Vertical Speed Indicator at moment $t$
* $ALT(t)$: display on Altimeter at moment $t$
* $ASI(t)$: display on Air Speed Indicator at moment $t$
## Models
$
\begin{align}
ASI(t) & \propto P_p(t)-P_s(t) \\
ALT(t) & \propto A-P_s(t) \\
VSI(t) & \propto -\frac{d P_s(t)}{dt}
\end{align}
$
## Blocked Pitot
So, when the pitot tube is blocked, we get ($C$ a constant):
$
\begin{align}
ASI(t) & \propto C-P_s(t) \\
\end{align}
$
## Partially Blocked Pitot
When the pitot tube is blocked but the drain hole remains open, after pressure is equalized, it's approximately:
$
\begin{align}
ASI(t) & \propto P_s(t)-P_s(t)=0 \\
\end{align}
$
## Blocked Static
$
\begin{align}
ASI(t) & \propto P_p(t)-C \\
ALT(t) & \propto A-C \\
VSI(t) & \propto -\frac{d C}{dt} = 0
\end{align}
$
So the Altimeter freezes, the VSI reads 0, and the ASI will subtract too much (under-read) at higher altitudes and subtract too little (over-read) at lower altitudes.