Estimate the velocity of the groundwater flowing from a point 500 feet from a creek. The point is 50 feet above the surface of the creek and the permeability of the subsurface is approximately 10.5. Approximately how long would it take the groundwater to reach the creek?
To estimate the velocity of groundwater flowing from a point to a creek and calculate the approximate time it would take to reach the creek, we can use Darcy's Law.
Darcy's Law states that the velocity of groundwater flow (V) can be calculated using the equation:
V = (Q / A) / K
Where:
- Q is the discharge or flow rate of water in cubic feet per second (cfs).
- A is the cross-sectional area of flow perpendicular to the direction of flow in square feet (ft²).
- K is the hydraulic conductivity or permeability of the subsurface in feet per second (ft/s).
First, let's compute the discharge (Q). Since we are given the distance from the point to the creek, we can estimate the discharge as the average flow rate per unit width of the aquifer. In this case, the width is not specified, so let's assume a width of 10 feet for simplicity.
Q = (10 ft) * (V avg)
Next, we need to calculate the cross-sectional area (A). The area of flow is the product of the width and the vertical head difference between the point and the creek.
A = (10 ft) * (50 ft) = 500 ft²
Now, let's calculate the velocity (V) using Darcy's Law by rearranging the equation:
V = (Q / A) / K
Since we don't have the exact permeability value (K), we can only make an approximate estimate based on the given information. Let's assume K = 10.5 ft/s.
Substituting the values into the equation:
V = ((10 ft * V avg) / 500 ft²) / 10.5 ft/s
To simplify the equation, let's cancel out the units and rearrange:
V = (V avg / 50) / 10.5
Now, let's solve for V using the given values. Since we are estimating, we will not be able to find an exact value, but we can still provide an estimate.
V = (V avg / 50) / 10.5
Based on the given information, we have:
- Distance from point to creek = 500 ft
- Vertical head difference = 50 ft
- Permeability = 10.5
By substituting these values, we can solve for the estimated velocity, V.
Please note that this calculation assumes certain assumptions and simplifications, and it is always better to have more accurate and detailed data for a precise estimation.