5 AP Physics 1 Fluid Problems Solved with a TI-84 Program

Martin McSweeney

 

Fluid mechanics can feel messy in AP Physics 1 because the formulas look similar and the variables start blending together. Density, pressure, hydrostatic pressure, buoyant force, and continuity all show up in the same unit — and under test pressure, it is easy to grab the wrong equation.

In this post (and the video above), I walk through 5 AP Physics 1 fluid mechanics problems using the MECH2 program for the TI-84 Plus CE. Each one shows the TI-84 input, the result, and the equation worked out by hand so you can see how they match.

The program is part of the Physics Mechanics Bundle — and also included in the AP Physics Ultimate Bundle and the AP STEM Mega Bundle.

Also, through Monday, March 30, 2026, you can get 25% off the AP Science Mega Bundle with code SCI25.

Problem 1: Density — rho = m / V

A block has a mass of 2.4 kg and a volume of 0.003 m^3. What is its density?

TI-84 path: Mechanics 2 → Fluids → Density → rho = m / V

Inputs:

  • m = 2.4
  • V = 0.003

Result: rho = 800 kg/m^3

By hand:

rho = m / V
rho = 2.4 / 0.003
rho = 800 kg/m^3

This is the most direct fluids formula in the unit. If you know mass and volume, density is just their ratio.

Problem 2: Pressure — P = F / A

A force of 120 N is applied uniformly over an area of 0.040 m^2. What pressure is produced?

TI-84 path: Fluids → Pressure → P = F / A → Solve for P

Inputs:

  • F = 120
  • A = 0.040

Result: P = 3000 Pa

By hand:

P = F / A
P = 120 / 0.040
P = 3000 Pa

This is a standard AP Physics 1 pressure problem. Same force over less area means more pressure.

Problem 3: Hydrostatic Pressure — P = P0 + rho*g*h

Water has density 1000 kg/m^3. What is the pressure at a depth of 5.0 m below the surface if atmospheric pressure is 1.01 × 10^5 Pa? Use g = 10 m/s^2.

TI-84 path: Fluids → Pressure → Hydrostatic P → P = P0 + rho*g*h

Inputs:

  • P0 = 1.01E5
  • rho = 1000
  • g = 10
  • h = 5.0

Result: P = 1.51E5 Pa

By hand:

P = P0 + rho*g*h
P = 1.01 x 10^5 + (1000)(10)(5.0)
P = 1.01 x 10^5 + 5.0 x 10^4
P = 1.51 x 10^5 Pa

This is a nice reminder that pressure below the surface is not just rho*g*h. Total pressure includes the pressure already present at the surface.

Problem 4: Buoyant Force — Fb = rho*g*V

An object displaces 0.020 m^3 of water. What buoyant force acts on it? Use water density 1000 kg/m^3 and g = 10 m/s^2.

TI-84 path: Fluids → Buoyancy → Fb = rho*g*V → Solve for Fb

Inputs:

  • rho = 1000
  • g = 10
  • V = 0.020

Result: Fb = 200 N

By hand:

Fb = rho*g*V
Fb = (1000)(10)(0.020)
Fb = 200 N

This is an Archimedes-principle type problem. The buoyant force equals the weight of the displaced fluid.

Problem 5: Continuity Equation — A1v1 = A2v2

Water flows through a pipe. At one point, the cross-sectional area is 0.030 m^2 and the speed is 2.0 m/s. The pipe narrows to 0.010 m^2. What is the new speed?

TI-84 path: Fluids → Continuity → A1v1 = A2v2 → Find v2

Inputs:

  • A1 = 0.030
  • v1 = 2.0
  • A2 = 0.010

Result: v2 = 6.0 m/s

By hand:

v2 = (A1*v1) / A2
v2 = (0.030)(2.0) / 0.010
v2 = 6.0 m/s

This is one of the key ideas in continuity problems: when the pipe gets narrower, the fluid moves faster.

Summary

Here is a quick reference for the five formulas covered:

Topic Formula
Density rho = m / V
Pressure P = F / A
Hydrostatic Pressure P = P0 + rho*g*h
Buoyant Force Fb = rho*g*V
Continuity Equation A1v1 = A2v2

If fluid mechanics feels like a lot to juggle, that is because it is. Multiple formulas, lots of symbols, and easy ways to make small mistakes. Having the program handle the arithmetic lets you focus on choosing the right equation and understanding what the physics means.

Get the Program

The MECH2 program is part of the Physics Mechanics Bundle for the TI-84 Plus CE. It also covers springs, momentum, rotational motion, and more — useful for AP Physics 1 review.

For broader exam coverage:

Discount through Monday, March 30, 2026: Use code SCI25 for 25% off the AP Science Mega Bundle.

New to TI-84 programs? Start with the Complete Install Guide (2026) or watch the install and troubleshoot video.

Questions about whether programs are allowed on your exam? See: Are TI-84 programs legal on AP exams?

AP® is a trademark registered by the College Board, which is not affiliated with and does not endorse this product.

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