Water flows through a pipe AB of diameter d1= 60mm, which is in series with a pipe BC of diameter d2= 85mm in which the mean velocity V2 = 3m/s. At C the pipe forks and one branch CD is of diameter d3 such that the mean velocity V3 is 2.5 m/s. The other branch CE is of diameter d4= 40mm and conditions are such that the discharge Q2 from BC divides so that Q4= ½ Q3. Determine Q1, Q3, Q4 and d3.

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Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.