Question

In the USA the unit gpd/sqft (gallon per day per square foot) is sometimes used to measure the hydraulic conductivity $k$, and the specific discharge q. What is the relation with the SI-unit $\mathrm{m}/\mathrm{s}$ ?

Short answer

Answer: 1 gpd/sqft ≈ 4.719 x 10^-8 m/s

Step-by-step solution

Identify unit conversions

To convert from gpd/sqft to m/s, we need to convert gallons to cubic meters and square feet to square meters. 1 gallon = $0.00378541$ cubic meters 1 square foot = $0.092903$ square meters

Convert gpd/sqft to cubic meters per day per square meter

Start by converting gallons per day to cubic meters per day (multiply by 0.00378541): 1 gpd = $1\ast 0.00378541=0.00378541$ cubic meters per day Next, convert square feet to square meters (multiply by 0.092903): 1 sqft = $1\ast 0.092903=0.092903$ square meters Now, divide cubic meters per day by square meters: $\frac{0.00378541{\mathrm{m}}^3/\mathrm{day}}{0.092903{\mathrm{m}}^2}=\frac{0.00378541}{0.092903}(\frac{{\mathrm{m}}^3}{{\mathrm{m}}^2\cdot \mathrm{day}})$

Convert cubic meters per day per square meter to m/s

Finally, convert from days to seconds: 1 day = 86400 seconds Divide the fraction obtained in step 2 by 86400 to get m/s: $\frac{0.00378541}{0.092903}(\frac{{\mathrm{m}}^3}{{\mathrm{m}}^2\cdot \mathrm{day}})\ast \frac{1\mathrm{day}}{86400\mathrm{s}}=\frac{0.00378541}{0.092903\ast 86400}(\frac{{\mathrm{m}}^3}{{\mathrm{m}}^2\cdot \mathrm{s}})$ Simplify the fraction to obtain the conversion factor between gpd/sqft and m/s: $\frac{0.00378541}{0.092903\ast 86400}\approx 4.719\times {10}^{-8}(\frac{\mathrm{m}}{\mathrm{s}})$

Conclusion

The relation between gpd/sqft and m/s for both the hydraulic conductivity (k) and the specific discharge (q) is: 1 gpd/sqft $\approx 4.719\times {10}^{-8}\frac{\mathrm{m}}{\mathrm{s}}$