Pressure and depth lab | Mistake Master Studio

The situation

A pressure probe hangs in a tank of still fluid. The deeper you lower it, the harder the fluid pushes on it, and the gauge climbs. How fast the gauge climbs with depth depends on the fluid: a denser fluid weighs more per meter of depth, so it pushes harder. Below you get a working tank with three knobs: the probe depth d, the tank width w, and which fluid fills the tank. A gauge reads the pressure in pascals.

First, commit to a prediction. Then the apparatus unlocks.

Predict first

Commit before you touch the sliders

Which changes make the gauge read a larger pressure? Check all you expect to. Lowering the probe to a greater depth Using a wider tank Filling the tank with a denser fluid

Plot the gauge pressure versus depth. What shape do you expect? A straight line through the origin (P is directly proportional to d) A curve that steepens as d grows (P is proportional to the square of d) A flat line (depth has no effect)

Explore

Test your prediction on the apparatus

Drag the sliders, switch fluids, and read the gauge at different settings. Or pick a test chip to lock everything but one variable and watch its relationship with the pressure draw itself. The fluid is still, so the gauge holds steady. Re-reading at identical settings repeats exactly, so any change you see is real.

Probe depth dd = 0.50 m

Tank width ww = 0.40 m

Fluid

Sealed tank: fluid = ?

Gauge pressure vs depth

Drag the unlocked slider. Every setting you visit drops a measured point.

Which fit matches your points?

Measure and read the slope

Which fluid is in the tank?

The tank has been sealed and its fluid tinted out, so you cannot tell what it is by looking. The gauge and the depth probe still work. Choose at least 5 different depths, read the gauge at each, and enter each (d, P) pair below. Then work through Read the slope: your points come out on a straight line right away, so there is no transform to hunt for here; the slope carries the density, and the walkthrough hands it to you once you can say why.

Fill the table with at least 5 depths, then work through the Read the slope steps. They lead you from the pressure equation to the slope rho g and on to the fluid density. Finish them and the Record button turns on and checks your density against the sealed fluid.

Transfer

One changed variable

Back on the open tank, suppose you lower the probe to twice the depth in the same fluid. Using the same relationship, by what factor does the gauge pressure change?

P is directly proportional to d, so twice the depth gives twice the pressure, because P = rho g d and only the depth changed. Two more things your sliders showed: a denser fluid at the same depth reads higher, since it weighs more per meter of depth, which is why the fluid sets the slope. And the tank width never entered the reasoning, so a narrow tube and a wide tank of the same fluid read the same pressure at the same depth.