Final answer:
The actual flow rate in a pipe is less than the theoretical flow rate due to energy loss from friction. Factors like viscosity, turbulence, and elevation changes also contribute to energy loss. The continuity equation dictates that flow rate through a constriction increases inversely with the square of the diameter reduction.
Step-by-step explanation:
The actual flow rate through a pipe is always less than the theoretical flow rate determined from the simplified Bernoulli's Equation due to a loss of fluid energy caused primarily by friction. Other factors that can cause a loss in flow rate include viscosity, turbulence, and changes in elevation, which affects the kinetic and potential energy of the fluid.
In fluid dynamics, the flow rate (Q) of an incompressible fluid through a constriction is given by Q = Av, where A is the cross-sectional area and v is the velocity of the fluid. According to the continuity equation, the product of the cross-sectional area and the velocity must remain constant throughout the flow. Therefore, when the cross-sectional area of a pipe decreases, such as in a Venturi tube, the flow speed increases to maintain a constant flow rate. This increase in speed is inversely proportional to the square of the decrease in diameter because the area is proportional to the square of the diameter.