Given a discharge Q and diameter D, which expression correctly gives the velocity V in the pipe?

• A. V = Q * (π D^2 / 4).
• B. V = π D^2 / 4.
• C. V = Q / (π D^2 / 4).
• D. V = Q / D.

Answer: (C)

Velocity in a pipe comes from the relation Q = V × A, where Q is discharge and A is the cross-sectional area. To get V, rearrange to V = Q / A. For a circular pipe, A = π (D/2)^2 = π D^2 / 4. Substituting gives V = Q / (π D^2 / 4). This is the correct form because it links the discharge to velocity through the actual flow area. The other forms mix in the area incorrectly or omit the area entirely: multiplying Q by the area would yield inconsistent units, using only the area ignores Q, and dividing by D alone ignores the D^2 dependence of the area.