Question

Water is flowing through a long horizontal tube. Let PA and PB be the pressures at two points A and B of the tube.
(a) PA must be equal to PB.
(b) PA must be greater than PB.
(c) PA must be smaller than PB.
(d) PA = PB only if the cross-sectional area at A and B are equal.

Answer 1

(d) PA = PB only if the cross-sectional area at A and B are equal.

Explanation:

• As per the Bernoulli’s Principle, the relation between pressure, kinetic energy and gravitational potential energy of a fluid in a container is
• p + 1/2 ρ v2 + ρgh =constant
• In the above formula p (pressure exerted by the fluid), ρ (density of the fluid), g (gravitational strength) and h( height of the container hA = hB) are same at both the points A and B in the long horizontal tube.  
• But the factor v (velocity of the fluid) is entirely depends on the cross-sectional area at the point. i.e. When the area of cross-section at two points is same, only then the velocity will be equal.  
• So, PA = PB only if the cross-sectional area at A and B are equal.