Cannot Find a Specific Form of Pump's Inertia Equation

Using SI units

Equation 1 states that moment (N.m) = M of I (kg.m²)*angular acceleration (rad/s²). (n-dot is in rev/s, hence the 2*pi)

Equation 2 states that power (watt) = moment*angular velocity (rad/s)*efficiency = pressure rise (N/m² or Pa)*flow (m³/s)

In KSB's example, 90% efficiency seems a touch optimistic.

I have a go at it...

Equation 1: n is rotational speed in radians/sec. n with a dot over it is dn/dt, rotational acceleration (in this case, deceleration).

Multiply rotational acceleration (n dot) by moment of inertia (J) gives torque. Torque times angle gives energy. Mp = 2*pi*J*(dn/dt) is the amount of energy removed from the water by the pump in one revolution decelerating at a rate of dn/dt.

Equation 2: Δp is the change in pressure calculated by the Joukowsky equation. Q is the flow rate given. Δp x Q is the amount of energy extracted by the stopped pump and dividing by 2*pi*n₀ normalizes it to one revolution of the pump. η, of course, is the efficiency.

Assuming constant deceleration, dn/dt = n₀/Δt, where Δt is the stopping time.

Setting the right-hand side of both equations equal and substituting n₀/Δt for dn/dt, we can solve for Δt.

Thanks you gentleman ...extreme thanks