Water Stream Narrows – Rankers Physics

Fluid Dynamics: Practice Problem & Solution

Assertion (A): The stream of water emerging from a water tap "necks down" as it falls. Reason (R): The volume flow rate at different levels is same.  
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Fluid Dynamics. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Continuity equation for fluid flow. For an incompressible fluid in steady flow, the volume flow rate \(AV\) (Area × Velocity) must remain constant. As water falls, its velocity \(V\) increases due to gravity, therefore, its cross-sectional area \(A\) must decrease, causing it to 'neck down'. Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R) Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring Reason (R): A coil spring of copper has more tensile strength than a steel spring of same dimensions. In the light of the above statements, choose the most appropriate answer from the options given below : (2022)
2. A small sphere of radius '$r$' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to : (2018)
3. The work done in blowing a soap bubble of \(20\text{ cm}\) radius is (surface tension of soap solution is \(0.03\text{ N/m}\))
4. The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied? (2013)
5. A uniform rope of density \(rho\) and length \(L\) is hanging from roof. If young's modulus of material of rope is \(Y\), then elongation produced in rope due to its own weight is: