(Fluid Mechanics) Collecting Sea Samples With Balloons

You're part of a team designing an autonomous submarine. The submarine collects seafloor samples at a location 30 meters below the surface.

To maximize collections, the submarine is designed such that when a suitable sample is encountered, the submarine inflates a balloon filled with pure oxygen at 10˚C that carries the sample to the surface for the team to immediately collect.

You're in charge of designing the collection system, and trying to figure out the balloon specifications. If the balloon expands too much, it could pop and the sample would be lost.

Your teammate currently has programmed the submarine to inflate the balloon to a volume of 3000 centimeters cubed at sea bottom, and the balloons you've been looking at expand to a max volume of 10,000 centimeters cubed.

Will everything work out dandy?

(If you don't know after 5 min...guess! Then learn from the solution for next time!)

(Physics) Traffic Intersection Accident

You've been hired to confirm the witness reports of a traffic accident case. 

Reports say that the 3-ton truck was headed eastbound at 60 MPH. The driver didn't see the light and ran the red. Witnesses then say it collided with a larger 8-ton delivery van going northbound at 35 MPH.

If that's so, what should be the final direction and speed of the allegedly guilty truck?

(Fluid Mechanics) Calculating Head Loss

A Quick Primer

In the real world where friction is a significant contributor, fluids will experience some energy density or pressure loss in whatever (pipe, surface, etc.) they flow through.

(Note: energy density [ $ \frac{J}{m^3} = \frac{N*m}{m^3} = \frac{N}{m^2} $ ] and pressure [ $ \frac{N}{m^{2}} $ ] have the same units.) 

In the industry, this is sometimes measured by the head loss, which is in units of meters. The concept of using units of distance to measure pressure loss is similar to how a manometer's pressure reading depends on the height of the indicating fluid.

Darcy-Weisbach Equation

One way we can calculate the head loss is through the Darcy-Weisbach Equation (below). This equation can be used for both laminar and turbulent conditions.


h = head loss due to friction [meters]
f = Darcy friction factor [dimensionless]
L = pipe length [meters]
v = average flow velocity [m/s]
D = pipe hydraulic diameter [meters]
g = local acceleration due to gravity [ $ m/s^{2} $ ]

(Derivation using dimensional analysis here. Ask us if you need clarification.) 

So many variables! Usually pipe length, flow velocity, and diameter are given or measured. You just might need to convert the cross section perimeter to a hydraulic diameter and make sure you have the flow velocity (not the volumetric flow rate). Gravity's a constant of 9.8 $ m/s^{2} $ , assuming you're not somewhere else like Mars.

To calculate the Darcy friction factor, review the below:

  1. Reynold's Number (to determine whether the flow is laminar or turbulent)
  2. Moody diagram (which tells you which Darcy friction factor f to use)
  3. Resource on hydraulic diameter

Groovy. That's all the puzzle pieces. Now let's put on those sexy safety goggles, and dive right in.

Your fancy faucet calculations are almost done - just one more step.  Previously, we found that the Darcy friction factor was 0.032. The pipe has an oval cross section with a hydraulic diameter of 5 cm, and section length of 0.65 m long. The water will be flowing around 1.25 m/s.

So what do you get when you calculate the head loss?

Use latex to write equations.

(Physics) Eureka! Mechanically Advantaged...

For a change of pace, you spend a weeklong vacation away from the drudges of your desk to take your hand in drudging up some fortune in Alaska's Yukon Gold Rush

And...Eureka! You strike the motherlode!!! You load up the gold onto a platform. You arrange the pulleys as shown above to try to make things easier on the motor hauling up your riches.

With this setup, what's the minimum force (equal to tension T at pulley A) it takes to lift the load?

      100 N
      300 N
      400 N
      600 N

(Physics) Force

A 30 pound force acts on the end of the 3 foot lever. Find the moment of the force about O.