Five fair coins are flipped .if the outcomes are assumed independent ,find the probability mass function of the number of heads obtained

Centrifugal pumps are the most commonly used in process industries. a rotodynamic pump in its simplest form consists of an impeller rotating inside a casing. the rotation of the impeller imparts a high-velocity head (or fluid height h=p /pg) to the fluid and converts this to an increased pressure upon discharge. centrifugal pumps are used for lower pressures and can deliver liquid at uniform pressure without shocks or pulsations. a fluid (p 790 kg/m3) is directed through a cylindrical pipe (di 10.0 cm) into a reciprocating pump and is discharged through another cylindrical pipe with diameter of 20.0 cm. if the initial average hydraulic velocity of the fluid is 12.5 m/s, find (a.) the initial volumetric flow rate of the fluid in m/min, (b.) the mass flow rate of the fluid in kg/min, (c.) the final volumetric flow rate of the fluid in m/min and (d.) the fluid velocity within the second pipe in m/s. provide all assumptions.