Using Slichter’s velocity relation for groundwater flow, compute the seepage velocity given: viscosity factor = 1.00, Slichter’s constant C = 400, effective size d = 0.5 mm, and hydraulic gradient i = 1/80. Choose the closest value (m/day).

Introduction / Context:
Empirical groundwater-flow relations like Slichter’s are useful for quick estimates of seepage velocity in granular aquifers when effective size and gradient are known. This problem applies the standard form to obtain a daily velocity.

Given Data / Assumptions:

• Viscosity factor (temperature corrected) = 1.00 (typical reference condition).
• Slichter’s constant C = 400.
• Effective grain size d = 0.5 mm.
• Hydraulic gradient i = 1/80 = 0.0125.
• Use the common form v = C * i * d^2 with d in mm and v in m/day.

Concept / Approach:
Slichter’s empirical velocity relation is expressed as:
v = C * i * d^2where v is the apparent seepage velocity (m/day), i is hydraulic gradient, d is effective size (mm), and C is a temperature-dependent constant (dimension-adjusted). With the viscosity factor set to 1.00, we use the supplied C directly.

Step-by-Step Solution:

Verification / Alternative check:
Order of magnitude is reasonable for coarse sand under a mild gradient; daily seepage of about a meter is credible in such materials.

Why Other Options Are Wrong:

• Values < 1 m/day (0.25, 0.50, 0.75) underestimate the computed result.
• 1.00 m/day is close but still below the exact calculation.

Common Pitfalls:

• Using d in meters rather than millimeters in the Slichter form provided with C.
• Forgetting to square the grain size.

Final Answer:
1.25 m/day