In a fire-suppression system, a main supply pipe of diameter 5.0 cm delivers water at a speed of 2.0 m s−1. Immediately after entering the building, the pipe divides into two branches that feed sprinklers on two different floors.
• Branch 1: diameter 3.0 cm.
• Branch 2: diameter 4.0 cm.
A flow sensor installed in Branch 1 reads a volumetric flow rate of 1.70×10−3m3s−1. The water is assumed incompressible and the flow is steady.
(a) Verify that the sensor reading in Branch 1 is consistent with the stated diameter and an average speed of 2.4 m s−1. Show your calculations.
(b) Determine the volumetric flow rate and average speed of the water in Branch 2.
(c) Calculate the percentage of the total inlet mass flow that is delivered to each branch. Comment on any practical considerations this distribution might raise for the design of the sprinkler system.