Two students suggest the following alternative expressions for the hydrostatic…
PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors
Problem
Two students suggest the following alternative expressions for the hydrostatic pressure P at a depth h below the free surface of a liquid of uniform density ρ:
Student A: P=ρgh2
Student B: P=ρgh
Analyse the two expressions and answer the questions below.
(i) Using dimensional considerations, decide which expression is dimensionally consistent.
(ii) Point out the dimensional inconsistency (if any) in the other expression.
(iii) For the dimensionally correct expression, calculate the absolute pressure at a depth of 40m in water. Take ρ=1000kg m−3, g=9.8m s−2 and atmospheric pressure P0=1.0×105Pa. Express your answer as the total pressure at that depth.