Flow in Accelerated Straight Circular Cross Section Pipe

Some pipe flow vs. pressure drop formulas include Hazen-Williams, Darcy-Weisbach, and Colebrook. One might start with those, adding or subtracting the vertical head over the distance of the sloped pipe run.

Yep. Incompressible flow. Darcy-Weisbach rocks!

Not only that; it's the easiest one of the lot!

Here on earth, at a constant velocity, gravity trumps inertia so there is no effect on the flow rate because of the "acceleration" of the system.

You could, perhaps, make a case that if the earth stands still the effect of gravity on the fluid inside the system would be slightly higher.

Now, if you want to consider what happens in a rocket's fuel delivery system at launch, due to the forces of acceleration, we can have a discussion about that.

Using Darcy-Weisbach (as others have suggested) you need to do an iterative calculation to find flow with a given pressure difference, even in the absence of acceleration.

If the pipe is accelerating, and pipe axis parallel to the acceleration, the force seen by the fluid = M*a = L*ρ*A*a, where M = fluid mass, L = pipe length, ρ = fluid density and a = acceleration. So ΔP due to the acceleration = force/area = L*ρ*a.

You can add that to your original ΔP to put into Darcy-Weisbach.

That's my take on it anyway.

I'd go with that - but it's a bit more complicated if the pipe axis isn't parallel to the acceleration. Need the OP to clarify - pipe inclined to the horizontal, but accelerating "in the forward direction" - which way's forward?

(Think you missed out "A = pipe cross-sectional area").

You're right, I forgot A = pipe cross-sectional area thanks.

If the pipe axis is at angle θ from the acceleration, the ΔP due to the acceleration is L*ρ*a*cos θ = L*ρ*a when θ = 0°, 0 when θ = 90°.