How Long Does a Brick Take to Sink to the Ocean Bottom? A Physics Model

Two Children Debate Bricks

Confucius walks by the sea and sees two fishing children arguing about how long a brick will take to reach the bottom when thrown into the water.

One child thinks it sinks instantly, another thinks it takes a long time, and they discuss gravity, water resistance, and depth.

Confucius remarks that the sinking time depends on sea depth, brick shape, density, and water properties, and that mathematics is needed to calculate it.

Note: This Confucius is not the historical figure.

Mathematical Model

To answer “How long does a brick take to sink?”, we must consider gravity, buoyancy, and drag, and build a model to estimate the sinking time.

Basic Assumptions

The brick is assumed to be a standard rectangular solid with uniform density.

Sea water is assumed to be stationary with constant density and viscosity.

We consider gravity, buoyancy and drag, ignoring currents and other effects.

Kinetic Equation

The motion is described by Newton’s second law, combining gravity, buoyancy and drag forces. When the brick reaches terminal velocity, the forces balance and it descends at constant speed.

Buoyancy

Buoyancy is calculated from Archimedes’ principle: the upward force equals the weight of the displaced water.

F_b is buoyancy.

ρ_w is water density.

g is gravitational acceleration.

V is the volume of the brick (or displaced water).

Drag

Drag depends on water density, the brick’s speed, drag coefficient, projected area, viscosity and characteristic length.

F_d is drag.

ρ_w is water density.

v is relative speed.

C_d is drag coefficient.

S is projected area.

μ is viscosity.

L is characteristic length.

Terminal Velocity

From the balance of forces, terminal velocity can be expressed as a function of brick mass, gravity, buoyancy, drag coefficient, water density and projected area.

Calculation Results

Using typical brick dimensions (24 cm × 11.5 cm × 5.3 cm) and density (1.8 g/cm³), together with average sea‑water density and a drag coefficient of 0.47, we estimate terminal velocities for two extreme projected areas.

<code>import math

# parameters
m = 2.633  # brick mass in kg
g = 9.8    # gravity m/s^2
rho_w = 1030  # water density kg/m^3
V = 0.0014628  # brick volume m^3
C = 0.47   # drag coefficient
S_max = 0.0276  # max projected area m^2
S_min = 0.006095  # min projected area m^2

def calculate_terminal_velocity(S):
    return math.sqrt(2 * (m * g - rho_w * g * V) / (C * rho_w * S))

v_t_max = calculate_terminal_velocity(S_max)
v_t_min = calculate_terminal_velocity(S_min)

v_t_max, v_t_min
</code>

The terminal velocity is about 5.2 m/s for the minimum projected area and about 2.9 m/s for the maximum projected area (values illustrative).

To compute total sinking time we consider the short acceleration phase (≈2 s) and then the constant‑velocity descent. Using average depths of the four major oceans, the estimated times are:

Pacific Ocean: ~1464 s (min speed) to ~3113 s (max speed)

Atlantic Ocean: ~1334 s to ~2838 s

Indian Ocean: ~1369 s to ~2912 s

Arctic Ocean: ~442 s to ~939 s

The Arctic Ocean yields the shortest time because of its shallower average depth, while the Pacific takes the longest. These estimates rely on simplified assumptions; actual times may vary due to currents, brick orientation, and other factors.

Reference: 魅力科学君 (2024), 列御寇 (2016).