Laminar and Turbulent Flow of Water Through Sand

The flow of water through sands during turbulence is represented by vⁿ=k'i in which v is the velocity of flow; i the hydraulic gradient; k', a coefficient of turbulence; and n, a turbulence exponent. Values of n and k' are obtained from a plot of constant head permeability tests on four sands, shown as log-log plot of velocity versus hydraulic gradient. For truly laminar flow, n equals 1. For sands with d₁₀ > 0.03 cms, the value of n is greater than 1, indicating turbulent flow. The value of n varies with grain size and hydraulic gradient. A plot of Reynold's number versus Friction Factor shows turbulent flow in one case of sand (d₁₀ = 0.03 cm) with Reynold's number substantially less than 1. A method is shown for conducting variable head tests for turbulent flow. The quantity of seepage through sand during turbulent flow can be calculated using the appropriate values of k' and n determined in the laboratory by the procedures outlined herein.