The specific capacity of an open well has the dimension of
- AL –1
- BT –1Correct
- CLT –1
- DTL –1
Solution
Concept
Specific Capacity of an Open Well
Formula
S = Q / s
Step-by-step solution
Step 1: Write the formula for specific capacity per unit area: S = Q / (A × s), where Q is discharge, A is area, and s is drawdown. Step 2: Substitute the dimensional formulas: Q = [L³T⁻¹], A = [L²], and s = [L]. Step 3: Simplify the dimensions: [L³T⁻¹] / ([L²] × [L]) = [T⁻¹].
Explanation
Specific capacity of an open well is defined as the discharge (water flow rate) per unit area per unit drawdown. - Discharge has dimensions of volume per time: L³ T⁻¹ - Area has dimensions of area: L² - Drawdown has dimensions of length: LDividing discharge by (area × drawdown) gives (L³ T⁻¹) / (L² × L) = T⁻¹. Thus, its dimension is T⁻¹ (per unit time).
Shortcut
Remember: Specific Capacity per unit area = Discharge / (Area × Drawdown) = (L³/T) / (L² × L) = 1/T = T⁻¹. Just remember it is inverse time (per unit time, T⁻¹).
Common mistake
Students often confuse specific capacity (discharge per unit drawdown) with specific yield or velocity, leading them to select LT–1 or mistakenly include length dimensions instead of calculating discharge per unit area per unit drawdown, which reduces to T–1.
Correct answer: B) T –1