So long as the pipe is full it doesn't matter if the pipe is up, down or flat.

Define your question better and add some drawings.

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If I want to know the pressure at P, can I simply determine the pressure drop along the pipe, assuming it's horizontal (and knowing Q, d and fluid viscosity), then subtract from that 0.4 psi per foot difference in height ?

The issue in something like that which is open to atmosphere is that the pressure drop in height h is usually more than the frictional losses unless you're flowing at a very fast velocity.

So if the negative number you get from your calculation is too high, the fluid vaporises at the top point / the pressure falls to less than atmospheric pressure.

Flow down vertical pipes is a world of its own and you normally need the Froude number to be less than 0.3 (I think)

But maybe if you explain why you're asking you can get a better answer.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

The question I was asked by a customer (and which I couldn't really answer), was 'knowing Q, h and the fluid viscosity, what's the minimum size of pipe that would be required to ensure zero back pressure at P ?'

Basically what you need is the smallest pipe where the frictional head losses in length of pipe h (actually h plus the length under the liquid level) at flow rate Q for viscosity V are lower than the head difference h. Note it's the pipe total length here that counts so if there are any horizontal bits, they count as well

So for different fluid viscosities you can usually either find a chart or calculate head loss for your length h. As you go down in size for the same Q the head loss goes up quite dramatically as you get smaller and smaller.

Does that make sense?

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

Yes, that makes sense.

Thank you