1. The problem statement, all variables and given/known data Problem Statement: Imagine you had a very long straw, one end is in the ocean (sea level) and the other end is in space. Air pressure at sea level is a standard atmospheric pressure and space is a perfect vacuum. Plot "height of water in straw" vs. time. Variables: h(t): height of water in straw (above sea level) at time t (in meters) A: cross-sectional area of straw (in meters^2) Starting conditions: At time 0, height of water is 0: h(0) = 0 At time 0, water has no velocity or acceleration 2. Relevant equations F = ma position(t) = position(0) + integral_0_t (velocity(0) + integral_0_t acceleration(t) dt) dt Standard atmospheric pressure is ~101,000 kg / (m * s^2) per unit area Density of water = 1,000.00 kg/m³ g = 9.8 m/s^2 3. The attempt at a solution Here is what I've tried and maybe someone can point out where I'm going wrong. net force = atmospheric pressure - force of gravity on mass of water in straw Atmospheric Pressure Standard atmospheric pressure is ~101,000 kg / (m * s^2) per unit area Let's call A the cross-sectional area of the straw (in meters^2). force of atmospheric pressure = 101,000 * A kg m/s^2 Force of gravity on mass of water in straw Force of gravity on water depends on how much water is in the straw (above sea level). Let's call h(t) the height of the water in the straw at time t. mass-of-water-in-straw(h(t)) = volume * density = h(t) * A * 1000 kg force_of_gravity(h(t)) = mass-of-water-in-straw(h(t)) * g = 1000 * h(t) * A * g kg m /s^2 F(t) = 101,000 * A - 1000 * h(t) * A * g m(t) = 1000 * A * h(t) (from mass of water equation above) So acceleration (F / m) = (101 - g * h(t)) / h(t) Written another way: a(t) = (101 - g * h(t)) / h(t) Ok, great, so I think h as a function of time should be the solution to this equation: h(t) = integral_0_t (integral_0_t a(t) dt) dt Substitution my equation for a(t), I get: h(t) = integral_0_t (integral_0_t (101 - g * h(t)) / h(t) dt) dt Unfortunately, I don't know how to solve that... so I tried to numerically approximate it. Let's just assume constant acceleration over short periods of time dt, then we can use much simpler equations and step through time in small dt steps. Simpler equations: a(t) = (101 - g * h(t-dt)) / h(t-dt) v(t) = v(t-dt) + a(t) * dt h(t) = h(t-dt) + v(t) * dt with starting conditions h(0) = 0 and v(0) = 0 and a(0) = 0 When I try to calculate my initial acceleration a(1), it's infinity (or rather, undefined) since the force of air pressure is pushing on no mass (no water is above sea level at the start of the problem)! There is obviously some flaw in that logic, but I'm not sure what it is. Any help is apprecated, thank you.