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c
Explanation: The various coefficient of hydrodynamic resistance is calculated along with
the volume of air passing per second. On substituting the various values and on addition
gives the total head produced.
The formula for the total head produced by a pump in a fluid system is described as a sum of different heads, reflecting varying energy forms according to the Bernoulli equation extended for pumps. The equation can be represented as follows:
[ H = H_s + H_p + H_{vp} + H_f ]
Where:
– (H) = Total head produced by the pump (meters of fluid or feet of fluid)
– (H_s) = Static head, the difference in height between the source and destination (meters or feet)
– (H_p) = Pressure head, representing the additional pressure added by the pump (calculated from the pressure the pump adds to the system, with units converted to meters or feet of fluid)
– (H_{vp}) = Velocity head, accounting for the velocity of the fluid leaving the pump (usually a smaller value in many pumping applications, calculated from the fluid velocity using (v^2 / (2g)), where (v) is velocity and (g) is acceleration due to gravity)
– (H_f) = Head loss due to friction in the pipes, which depends on the diameter and length of the pipes, the fluid’s kinematic viscosity, and the flow rate (meters or feet)
This total head calculation is crucial in the design and operation of fluid systems to ensure that pumps can meet the required flow rates and pressures. Understanding each component allows engineers to predict the performance of a pump in transferring fluid between