Water is flowing through a pipe whose cross sectional area at point a is larger than the cross sectional area at point b. the reading on a pressure gauge connected to the pipe at point a will be lower than the reading on a pressure gauge connected to the pipe at point b.
a. true
b. false

a. True

Explanation:

Pressure is always inversely proportional to the cross section area

This can be proven from the equation P = F/A

Where P = Pressure, F = Force and A = Cross-sectional area

This can also be similarly proven from the continuity equation given as

A₁V₁ = A₂V₂

Where A₁ = Area in first part of pipe (point A)

A₂ = Area in second part of pipe (point B)

V₁ = Velocity of water in first part of pipe (point A)

V₂ = Velocity of water in second part of pipe (point B)

From the continuity equation we can have that

V₁/V₂ = A₂/A₁

Thus the velocity of the liquid at any point in the pipe is inversely proportional to the cross-sectional area of the pipe. The liquid will be moving  slowly where the area is large and will be moving rapidly where the area  is small, and since the velocity is directly proportional to the force (F = m × v/t)which id in turn directly proportional to the pressure (P = F/A), this proves my answer to be True!

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