A diffuser in a pipe flow is essentially a gradual expansion in pipe diameter, which reduces fluid

velocity and increases pressure $($due to the Bernoulli effect$).$ Water at room temperature $(25C)$

flows through a horizontal diffuser at a rate of $40$ liters per second. The pipe diameter gradually

increases from $5$ cm at the inlet to $10$ cm at the outlet. The irreversible head loss across the

diffuser is estimated at $0\mathrm{.}35$ m $.$ The flow is turbulent, and the kinetic energy correction factors at

both the inlet and outlet are assumed to be $1\mathrm{.}05.$

$($a$)$ Calculate the pressure difference $P_2-P_1$ in units of kPa using the energy equation.

$($b$)$ Repeat the same using the Bernoulii equation $($ignoring irreversible head losses and kinetic

energy correction factors$).$ Calculate the percentage error in the result due to the Bernoulli

approximation.