Age of the Grand Canyon

Faith & Science Conversation
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No it wouldn’t. Not the kind of strata you see in the Grand Canyon at any rate.

Some of the strata in the Grand Canyon consist of sedimentary rocks such as shale, which are formed from very fine particles of silt (typically a few microns across). The rate at which these particles can fall through water is limited by Stokes’ Law:

F_d=6 \pi \mu R v \qquad [1]

where:

  • F_d is the drag on the particle
  • \mu is the viscosity of water
  • R is the radius of the particle
  • v is the speed at which it is falling.

The downward force on a particle is:

F_g = (\rho_p - \rho_w) g \frac 4 3 \pi R^3 \qquad [2]

where:

  • F_g is the downward force due to gravity, taking buoyancy into account
  • \rho_p is the density of the particle
  • \rho_w is the density of the water
  • g is the gravitational acceleration (9.81\text{ m/s}^2)

Combining [1] and [2] gives us the terminal velocity:

v = \frac{2}{9}\frac{\left(\rho_p - \rho_w\right)}{\mu} g\, R^2 \qquad [3]

For a particle of, say, quartz or feldspar, ten microns across, we have \mu \approx 1.3 \times 10^{-3} \text { Pa s}, R \approx 10^{-5} \text m, (\rho_p - \rho_w) \approx 1500 \text{ kg m}^{-3}. Plugging these numbers in gives us a quarter of a millimetre per second, or about one metre per hour.

The particles will simply not settle in currents significantly faster than this.

The upshot of this is that sedimentary strata such as shale can ONLY form over very long periods of time in very still water. This is not a process that can be accelerated either. If you decreased the viscosity, you would increase turbulence, making it all the more difficult for the particles to settle.

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