# Air pressure under water

I have a question that I had asked in the stack physics section and they told me that I should ask my question here.

So I am basically starting to work on an RC submarine, and I want to use a 200ml syringe as a ballast tank. My plan was to pull the syringe handle back with a gear system, that's being rotated by a small DC motor.

My question is: how can I calculate, how much force(Newtons) does the motor need to pull the handle back and suck water into that syringe?

After finding how much force it needs to pull, how can I calculate the minimal electrical power it needs to use in order for it to operate?

• Multiple questions packaged into a single one are generally now very welcomed, although your case is not very bad yet (there are people sending a regular question list in a single post...) I tried to fix your grammar. Good luck! Commented Feb 16, 2018 at 23:49
• I did try to separate all my questions by hitting the enter button, but that didn't seem to work, thank you anyways =)
– Z. H
Commented Feb 16, 2018 at 23:59
• Most of the load that you will have to deal with is down to the friction of the syringe ie the seal... Commented Feb 17, 2018 at 11:17

It depends on the air pressure inside your submarine and the maximum depth you want to operate at. Friction of the syringe will also have to be accounted for.

Lets say you want to dive 100meters max and the air pressure inside the unit is atmospheric (which cancels out the air pressure above the water).

We then calculate the hydrostatic pressure:
1000kg/m^3 *10m * 9.81m/s^2 = 98kPa

The force is dependent on the diameter of syringe. Looks like the diameter of a 200ml syringe is 44.75mm.

Area = 3.14159* ( 44.75mm/2 )^2 = 0.00157 m^2

Force = 98kPa * 0.00157 m^2 = 154N (~35 pounds force)

Note that this method considers the volume of the air in the submarine large compared to the volume in the syringe. The required force will be reduced by the increased air pressure in the submarine.

The static friction from the seal will also need to be measured empirically and added to the total force required. To estimate it, this link gives an overview of forces required for a range of syringes; recently-moved up to 3 year old. Based on their graph it looks like about 5 Newtons for a recently-moved (6 or 8mm diamete?) syringe. A 200ml syringe will be more than this and will need tested empirically with a scale.

Add the friction value to the total force required and multiply by a 1.5 safety factor.

Then just buy a linear actuator with the right force and stroke. Then just use the manufacturer specifications on power consumption as it already includes the gear/motor efficiency calculations. This FA-35-12-(X)-P linear actuator has a maximum draw of 5A at 12v or 60watts.

• citation/calculation needed for "It will probably be around 5 Newtons". Suggestion to use Linear Actuator instead of DC Motor is good. Commented Feb 19, 2018 at 15:43
• @Jonathan R Swift, Added citation in answer. Commented Feb 19, 2018 at 19:00
• Good citation - recommendation of safety factor in calculation also important. Commented Feb 19, 2018 at 19:03
• Keep in mind too that the system will not only have to move the plunger, but there will either need to be a shutoff valve on the water inlet to the plunger or the acuator will have to lock the plunger in place continually. Commented Feb 22, 2018 at 13:41
• @DLS3141, A high gear ratio actuator like this is usually a worm drive and doesn't require additional locking. Commented Feb 23, 2018 at 18:20

If energy consumption is important, a springloaded syringe may be effective. You only need to let go of it to submerge. That costs little power, so more is left for driving the boat. Refilling it with air again is an issue, but that could be done with a CO2 charge. You now, those used by airsoft and paintball pistols and what not. Again, you'd only have to open a valve to let in some CO2 and push out the water. That way, you can submerge and surface as often as you want without having to interact with the boat. (as long as the CO2 charge is not depleted of course..)

Just get a water meter, there are analog ones with an additional impulse output or a 4-20mA signal - where i live, 50-100€ a piece. A water meter without signal output might set you back 30€.

Other solutions are more complicated for a worse result:

• pump flow rate is pressure dependant, during a pumping cycle the water level in your well will sink and level in your tank will rise, flow will become lower.

• counting the pumping cycles as per ercnutschs answer would work better, with the caveats in his answer. You'd need to set up to simple sensors and homebrew a system to interpret the signals

• Since this is drinking water, any solution must be sure to no compromise water quality. Drinking water meters are made with this in mind.

In summary, I think an off-the shelf water meter is your best bet.

Your best bet is to calculate this experimentally. The friction of the syringe will likely completely dwarf the pressure requirements - unless you want your model to go deeper than a couple meters.

Use a dynamometer (or a spring weight) to determine force needed:

• to move the piston with free air access
• to double the volume with air access restricted (say, going from 5 to 10ml)

This way you'll get the force of friction and force of friction + 0.5 bar pressure differential. Subtract the first readout for pressure force alone. You're getting 1 bar per 10 meters of depth, so the force from pressure will be 0.2 x (your result) per meter of depth. (and your RC transmitter is unlikely to reach deeper than 2-3 meters deep anyway)

Knowing the force, the motor torque rating, your mechanical transmission between the torque and linear force (screw actuator?) and your motor power rating at max load, you'll know the power requirements - but you really should go with a pretty high safety factor, like 2x, because varying conditions like friction depending on temperature, sticky moisture, voltage drop, friction of the transmission etc will be large enough to break this in common operation easily.