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consider fully developed laminar flow in a circular pipe. if the diameter of the pipe is reduced by half while the flow rate and the pipe length are held constant, the head loss will (a) double, (b) triple, (c) quadruple, (d) increase by a factor of 8, or (e) increase by a factor of 16

Answer :

Each fluid particle moves along a streamline with a constant axial speed in fully developed laminar flow, and the velocity profile u(r) is unaffected by the flow direction.

The velocity component in the direction normal to flow is 0 everywhere because there is no motion in the radial direction. According to the continuity equation, we can increase the volume flow rate, or the velocity of the fluid passing through the pipe, by reducing the pipe's diameter. The radial distance from the pipe's center determines how much shear stress is present. As a result, the shear stress changes linearly with the radial distance for laminar flow through a round pipe.

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