A fluid‐flow textbook presents the expression p+ g h = constant where is pressure at…
PHYSICS · Subjective · CBSE · Physics · Units and Measurements · Units and Measurements
Problem
A fluid‐flow textbook presents the expression
p+ρgh=constant
where p is pressure at a point inside a static liquid, ρ is the density of the liquid, g is the acceleration due to gravity and h is the depth of the point below the free surface.
(i) Verify dimensionally that each term in the above expression can be meaningfully added.
(ii) While analysing a moving fluid, a third term 21ρv2 (where v is speed of the fluid element) is often included so that
p+ρgh+21ρv2=constant.
Show, by dimensional comparison, that the inclusion of this term preserves the validity of the addition.
(iii) Another student suggests adding the speed itself so that p+ρgh+v=constant. Show that this proposal violates dimensional consistency and hence is unacceptable.