NapkinCalc

Fluid Mechanics — Flow & Pressure

Pump power — the cost of pushing fluid uphill

continues from lesson 5 — values defined earlier in the course stay live here

ELI5: to lift a flow Q to a height H you must supply power P = ρ·g·Q·H. It's just "weight lifted per second" — the same energy bookkeeping as everything else, now for a moving fluid.

Qflow=A1⋅v1Q_{flow} = A_{1} \cdot v_{1} = 0.062832 m^3 / s volume flow rate through the wide pipe
Hhead:=20mH_{head} := 20 m = 20 m how high the pump must lift it
Ppump:=ρwater∗gacc∗Qflow∗HheadinkWP_{pump} := \rho _{water} * g_{acc} * Q_{flow} * H_{head} in kW = 12.328 kW hydraulic power ≈ 12.3 kW
✓ pass Ppump>0kWP_{pump} > 0 kW real power a motor must deliver (divide by efficiency for the rated size)

Try it yourself: the hydrostatic pressure at 25 m depth in water? (P = ρ·g·h, ρ = 1000 kg/m³, g = 9.81 m/s²; answer in kPa.)

Phydroyou:=1000kg/m3∗9.81m/s2∗25mPhydro_{you} := 1000 kg/m^3 * 9.81 m/s^2 * 25 m = 245250 Pa ✏️ Your turn: multiply density × gravity × depth (the result converts to kPa).
✓ pass abs(Phydroyou−1000kg/m3∗9.81m/s2∗25m)<1e−6kPaabs(Phydro_{you} - 1000 kg/m^3 * 9.81 m/s^2 * 25 m) < 1e-6 kPa green when your hydrostatic pressure is correct

That completes the Engineering track — statics, the stress inside materials, bending beams and buckling columns, the energy in heat and engines, and the fluids that flow through it all. Every formula here is live: change a number and watch the whole design respond.