Answer the following questions regarding the flow of an ideal incompressible fluid through a pipe of varying cross-section:
a. (i) State the equation of continuity for steady incompressible flow, clearly defining each symbol used.
b. (ii) A horizontal pipe tapers smoothly from an internal diameter of 8 cm to 4 cm. Explain, without doing any calculation, how the speed of the fluid changes as it moves from the wider to the narrower section.
c. (iii) A student argues that the volume flow rate must decrease in the narrower section because the area is smaller. Examine this statement and give a reasoned answer based on the principle involved.
d. (iv) Mention any two practical devices or situations where this area–velocity relationship of a fluid is put to use.