Calculating Permeability in a Tube of Horizontal Soil: Homework Question

[FChebli]

Homework Statement

A horizontal layer of soil in a tube 100 x 100 mm in cross-section. water is supplied to maintain a constant head difference of 300 mm across the sample. the coefficient of permeability of the soils in the direction of flow through them are as follows:
Soil A = 10^-2
Soil B = 3 x 10^-3
Soil C = 4.9 x 10^-4
Each of the soil samples width = 150 mm
Find the rate of supply in cm3/hr

Homework Equations

Kv(eq) = H / (H/K)a + (H/K)b + (H/K)c
q = k A dH/L

The Attempt at a Solution

Sub. with equation 1: K = 1.2 x 10^-3 cm/s
Sub. directly in equation 2 gives a wrong solution, what should I do?

 

[nate808]

Hello, thank you for your post. To find the rate of supply in cm3/hr, we first need to convert the permeability coefficients from cm/s to cm/hr. We can do this by multiplying each coefficient by 3600 (the number of seconds in an hour). This gives us:

Soil A = 36 cm/hr
Soil B = 10.8 cm/hr
Soil C = 1.764 cm/hr

Next, we can use the equation q = k A dH/L to find the rate of flow for each soil sample. Since the width of each sample is 150 mm, or 15 cm, we can plug in this value for A. The head difference, H, is given as 300 mm, or 30 cm. The length of the sample, L, is not specified, so we will assume it is 100 mm, or 10 cm.

For Soil A: q = (36 cm/hr)(15 cm)(30 cm)/(10 cm) = 1620 cm3/hr
For Soil B: q = (10.8 cm/hr)(15 cm)(30 cm)/(10 cm) = 486 cm3/hr
For Soil C: q = (1.764 cm/hr)(15 cm)(30 cm)/(10 cm) = 79.68 cm3/hr

Therefore, the total rate of supply for all three soil samples is 1620 + 486 + 79.68 = 2185.68 cm3/hr.

I hope this helps! Let me know if you have any further questions.