A question of fluid dynamics

[Rupert]

I was wondering if anyone could help me with something that's about to come up in my current campaign.

There's a transdimensional portal about to open near the party's location, and I'm wondering what effects this will have in terms of winds, etc.

The portal is an upright circle ~100m in diameter, in the open. It's set on a world with an atmospheric pressure of 0.7 atmospheres. The other side is in vacuum, and the portal may be assumed to be moving, or the air coming through pumped away, so it'll remain a hard vacuum for the duration of the event.

The questions are: How fast will the air move through the portal? At 100m distance and 300m distance, roughly right in front of the portal, how fast will that wind be?

And one more - in atmospheres of pressures different from Earth's nominal one atmosphere, how does the force exerted on a by wind person vary with pressure? Is it linear, or some power relationship?

Essentially, I'm wondering if the wind from the air rushing into this new void will be dangerous to the PCs, or if it will just sweep up any light, loose equipment, or will just be a bit of a wind going past them.

[martinl]

Originally Posted by Rupert

The portal is an upright circle ~100m in diameter, in the open. It's set on a world with an atmospheric pressure of 0.7 atmospheres. The other side is in vacuum, and the portal may be assumed to be moving, or the air coming through pumped away, so it'll remain a hard vacuum for the duration of the event.

...

I'm not up to doing that one in detail, but the force across the portal is roughly (scribble scribble) 0.5 GN, or around 100 million lbs, or a demi-Nimitz.

I doubt you are looking at a gentle breeze.

[lwcamp]

At the portal mouth, the air will be rushing into the void at the speed of sound. This will exert a force of about 65,000 newtons per square meter (using the formula for aerodynamic drag. This is fairly close to the difference in static pressures, or 100,000 newtons per square meter). For a typical frontal area of a human of about 0.5 m^2, this comes out to a force of about 3 tons.

If you consider two imaginary concentric spherical shells around the portal, and you assume the flow has reached steady state, then the total amount of air passing through each shell must be the same. The amount of air that passes through is given by the shell's area times the air's density at the shell times the air speed at the shell. If we assume that the air density doesn't change that much (which is good enough for a zeroth order approximation, although it probably breaks down very close to the portal), then we get that the air speed is inversely proportional to the shell area. Since the shell area grows as the square of the radius, the wind speed will fall off with the square of the distance from the portal. The aerodynamic drag exerted by the wind is proportional to the square of the wind speed, so the force exerted will drop with the fourth power of the distance to the portal.

Here's a quick, approximate chart

distance     wind speed        description
100 m        330 m/s           sonic airflow
170 m        120 m/s           F5 tornado: overwhelming devastation.
180 m        100 m/s           F4 tornado: extreme devastation.
200 m        80 m/s            Category 5 major hurricane, F3 tornado: severe devastation.
220 m        65 m/s            Category 5 major hurricane, F2 tornado: devastation. 
240 m        55 m/s            Category 4 major hurricane, F2 tornado: devastation.
260 m        50 m/s            Category 3 hurricane, F2 tornado: devastation.
290 m        40 m/s            Category 2 hurricane, F1 tornado: devastation.
315 m        35 m/s            Violent storm, category 1 hurricane, F1 tornado: widespread damage, 12-14 meter waves at sea.
350 m        27 m/s            Storm, F0 tornado: trees uprooted, considerable structural damage, 10 meter waves at sea. 
380 m        23 m/s            Strong gale: slight structural damage, 8 meter waves at sea.
400 m        20 m/s            Gale: twigs break off trees, generally impedes progress, 6 meter waves at sea. 
450 m        17 m/s            High wind: whole trees in motion, 5 meter waves at sea.
500 m        13 m/s            High wind: inconvenience felt when walking against the wind, 4 meter foamy breaking waves at sea.
570 m        10 m/s            Strong breeze: large branches in motion, whistling heard in strung wires, 3-4 meter cresting waves at sea, sea spray.
630 m        8 m/s             Fresh breeze: small leafy trees sway, cresting waves form on inland waters, 2-3 meter cresting waves at sea. 
700 m        7 m/s             Moderate breeze: raises dust and loose paper, small branches moved, 1-2 meter waves at sea.
800 m        5 m/s             Gentle breeze: leaves and small twigs in constant motion, 1 meter waves at sea.
1200 m       2.5 m/s           Light breeze: wind felt on face, leaves rustle, half-meter waves at sea. 
1800 m       1 m/s             Light air: air motion nearly imperceptible.

This is for earth air density, for a similar effect at 0.7 atmospheres of pressure, multiply all distances (except for sonic airflow) by sqrt(0.7) ~= 0.84.

Luke

[whswhs]

Hemispherical shells, perhaps, at least close to the portal?

[Rupert]

That's awesome! Thankyou very much.

That means that the two characters (by chance NPCs) 100m away sitting on their parked speeder are going for a dive, along with their speeder. The 3,000 ton spaceship sitting nearby (with its engines disabled) will, I expect, be dragged along the (smooth) ground until it goes in as well.

The PCs ~300m away on the ground will need to find shelter (and there's some nearby) lest the wind find things heavy enough to damage them. The ones ~300m and up on the side of a huge (1km per side) alien tetrahedron will be making lots of checks to not be torn off the structure. Fortunately for them they've got ropes anchored to pitons glued to the thing so they'll probably just get roughed up.

Should be an interesting opening to next session.

EDIT: Another thing occurred to me - how loud is this likely to be, aside from the noise the wind makes rushing past obstacles?

[malloyd]

Originally Posted by Rupert

The portal is an upright circle ~100m in diameter, in the open. It's set on a world with an atmospheric pressure of 0.7 atmospheres. The other side is in vacuum, and the portal may be assumed to be moving, or the air coming through pumped away, so it'll remain a hard vacuum for the duration of the event.

The questions are: How fast will the air move through the portal? At 100m distance and 300m distance, roughly right in front of the portal, how fast will that wind be?

Very roughly for any fluid flow the pressure difference = 1/2 (density)(velocity)^2. There are all kinds of modifications for nozzle shape, temperature changes, back pressure, friction, etc, but this works for order of magnitude type calculations.

Assuming the composition of terrestrial air (about 1.3 kg/m^3 at 1 atm) this should give you about

(0.7 - 0) atm x 101.3 kPa/atm = 1/2 (0.7 x 1.3) kg/m^3 x V^2
Or V = 197 m/s, or about 430 miles per hour at the entry/exit plane

To a first approximation the steady state should see the same amount of gas flowing through the portal as through spherical shells at various distances around it. So just the ratio of the areas. For a 100 meter circle vs a 300 meter sphere that's 4 * 3^2, so winds to there should average about 12 mph. For a 100 meter sphere it's just 4, so on *average* at 100 meters from the center speeds should be 43 mph, but of course that's much too close for the equilibrium to actually be established (half that sphere is entirely blocked to the hole for one thing!). Note this neglects any pressure drop, actual velocities should be expected to be higher and densities lower, but in terms of how much is it pushing stuff away those trade off fairly evenly. So yeah, if you are within 100 meters of either face there's a major storm force wind or greater trying to blow you through, or away from, the hole depending on which side you are on. For a hole that has *just* opened, you definitely are not at equilibrium, so it's presumably even worse.

And one more - in atmospheres of pressures different from Earth's nominal one atmosphere, how does the force exerted on a by wind person vary with pressure? Is it linear, or some power relationship?

Drag is more or less linear in air density, which is linear in pressure if the composition is the same.

[Daigoro]

Originally Posted by lwcamp

At the portal mouth, the air will be rushing into the void at the speed of sound.
<...>
100 m 330 m/s sonic airflow

Just to check, the speed at the portal mouth and at 100m away will both be at sonic speed?

[Daigoro]

Originally Posted by Rupert

The 3,000 ton spaceship sitting nearby (with its engines disabled) will, I expect, be dragged along the (smooth) ground until it goes in as well.

It might get buffeted, but that's a lot of weight. Also, is it streamlined? Is it pointing nose into the wind?

[Rupert]

Originally Posted by Daigoro

It might get buffeted, but that's a lot of weight. Also, is it streamlined? Is it pointing nose into the wind?

Streamlined, but the wind will hit it on the starboard (right) rear, and from that angle it being streamlined won't be helping a lot. Also, while heavy, it isn't very dense, so there'll be quite a bit of force though not nearly as much per unit mass as for a person (the square/cube 'law' helps the spaceship). Some quick and dirty maths suggests and it'll get pulled along the ground, as it's sitting on a solid, flat, and fairly smooth rock surface. Once it gets close enough it'll partially block the airflow, which will increase the pull on it (and it will fit through the portal, so it won't stop the 'fun' for everyone else).

[lwcamp]

Originally Posted by Daigoro

Just to check, the speed at the portal mouth and at 100m away will both be at sonic speed?

I intended 100 m away from the center. But that was with misreading that the radius was 100 m, rather than the diameter. So all the distances can be divided by 2,

Luke