A horizontal pipeline carrying water at steady flow splits into two outlet pipes at a…
PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids
Problem
A horizontal pipeline carrying water at steady flow splits into two outlet pipes at a T-junction. The inlet pipe has an internal radius of 2.0 cm, while each of the two outlet pipes has an internal radius of 1.4 cm. Assume the water is incompressible and the pipes remain completely filled throughout the flow.
Answer the following questions in a clear, logical sequence. Show all reasoning and use appropriate units.
(a) Identify the physical quantity that must be the same for the combination of the two outlet pipes as for the single inlet pipe when the flow is steady.
(b) Explain qualitatively why the sum of the volumetric flow rates in the two outlet pipes must equal the volumetric flow rate in the inlet pipe.
(c) Using only geometric information provided, determine the ratio of the speed of water in each outlet pipe to the speed of water in the inlet pipe. State any assumptions you make.
(d) A student claims that because the two outlet pipes have identical radii, the speed in each outlet must be half the inlet speed. Evaluate this claim with reference to your calculation in part (c) and explain any discrepancy.