To express the relationship where $p$ varies directly with $d$ and inversely with $u$, you can use the following equation:

$p = k \frac{d}{u}$

Here, $k$ is the constant of proportionality. This equation means that $p$ increases as $d$ increases and decreases as $u$ increases, with $k$ scaling the relationship.

If you have further questions or need more details on how this relationship works, feel free to ask!

Here are some related questions you might consider:

1. How would the equation change if $p$ also varies directly with another variable, say $v$?
2. What happens to $p$ if $d$ is doubled while $u$ remains constant?
3. How can you determine the value of $k$ given specific values for $p$, $d$, and $u$?
4. Can you provide a real-life scenario where such a relationship might be applicable?
5. What is the graphical representation of this relationship when $d$ and $u$ take on various values?

Tip: When dealing with direct and inverse variations, remember that the constant of proportionality $k$ holds the key to how the variables influence each other. Always check units and dimensional consistency in practical applications.