# Velocity of sinking submarine

Tags:
1. Jan 31, 2016

### vincekillics

1. The problem statement, all variables and given/known data
A small spherical under water ROV (remotely operated vehicle) has a radius of 0.5m and a mass of 450kg. It sinks or rises in the ocean by taking water on board or pumping it back out again. How much water must it take on board to sink at a constant velocity of 1.2m/s. The resistive force on it from the water is 130N. Assume the density of seawater is 1.03 x 103 kg/m3.

2. Relevant equations
P=ρgV/ρgh
F=mg

3. The attempt at a solution
First I tried to calculate the volume of the rov using 4/3 phi r^3, i got 0.52m^3
then I calculated the buoyancy force using ρgV and got 5254.236N and add up the resistive force of 130 N I got 5384.236N after this i dont know what to do

2. Jan 31, 2016

### SteamKing

Staff Emeritus
First thing to do is draw a free body diagram of the ROV and show all the forces acting on this vessel.

You are given the mass of the vessel (450 kg) and you have calculated the buoyant force. You are given the drag force when the ROV sinks (130 N). You'll need to calculate how much water the ROV needs to take on board so that it can sink. Remember, the drag force is developed only while the ROV is sinking.

3. Feb 1, 2016

### vincekillics

Hi, thanks for answering, but I still struggle to find the answer, I know that the rov would have to change its density to sink, the problem is I dont understand how to correlate the sinking velocity to the F=mg

4. Feb 1, 2016

### SteamKing

Staff Emeritus
If the submarine is sinking at constant velocity, what is its acceleration?

5. Feb 1, 2016

### vincekillics

must be 0m/s^2 right?

6. Feb 1, 2016

### SteamKing

Staff Emeritus
Correct.

And if the acceleration of the body is zero, what does this imply about the net force which acts on said body?

7. Feb 1, 2016

### vincekillics

net force should be 0 ? but Fmg > Fb on sinking object ?

8. Feb 1, 2016

### SteamKing

Staff Emeritus
Which is why you are asked to calculate how much water ballast to add to the ROV to get it to sink.

9. Jun 22, 2017

### msubby

There are many commercial models of ROV & AUV on the market today. A few have used variable ballast systems such as you have described, but not very successfully. VB systems are only suited to larger models weighing in the tons, due to the weight of the equipment required to effect the required changes. EG if you want to change the payload (water in this case) by 1 Ton. The equipment required to effect this change - motor, pump, pipework, valves, pressure resistant tank, would likely weigh close to a ton. Possibly even more for a very deep rated sub. Therefore it is a very inefficient means of changing depth. It only comes into its own when you get up to subs weighing 10T or more. ROVs these days use thrusters to change depth or Altitude) depending upon whether you're measuring from the seabed or the surface. Even large ROVs weighing 40T.

10. Jun 23, 2017

### haruspex

Yes, but the barest downward motion will do, so the net force can be as close to zero as you like.