Explain a pressure decrease with kinetic, height and loss terms

Declare the fluid, reference and evidence

Bernoulli’s ideal relation is an energy account along a streamline for steady incompressible flow with negligible dissipation. Each term p, ρv²/2 and ρgz has units J/m³, equivalent to Pa. Pressure work can become kinetic or gravitational energy; pressure itself is not a complete energy budget.

Build the algebraic model

The original packet holds flow at 0.002 m³/s. Inlet area 0.002 m² gives mean speed 1 m/s, while outlet area 0.001 m² gives 2 m/s. Inlet gauge pressure is 30000 Pa. With water density 1000 and g=10, the increased kinetic term uses 1500 Pa. Raising the outlet by z metres uses another 10000z Pa.

Check the original numerical packet

A prescribed nonnegative loss is added to the ideal account: p2=30000−1500−10000z−loss. At z=1 m and loss 5000 Pa, outlet gauge pressure is 13500 Pa. Multiplying each term by flow gives pressure-work decrease 33 W, partitioned into 3 W kinetic increase, 20 W height increase and 10 W irreversible mechanical-energy loss.

Challenge the assumptions and transfer

At z=2 m and loss 10000 Pa, the result is −1500 Pa gauge but 98500 Pa absolute under the supplied atmosphere. Negative gauge pressure is not negative absolute pressure. A pump supplying 10 W at this flow would add 5000 Pa of mechanical energy per volume, but this model includes no pump. The loss is stipulated rather than derived from ideal Bernoulli; neither pressure nor this ledger certifies a real installation, cavitation margin or fluid regime.

Worked original case

With zero elevation and zero loss, outlet gauge pressure is 28500 Pa. At unchanged flow, adding 2500 Pa loss lowers that pressure by 2500 Pa and converts 5 W of mechanical power.

Bounded investigation

Vary elevation while holding loss fixed, then vary loss at one elevation. Close the four-term power budget and distinguish reversible height or speed changes from the specified irreversible loss.

Changed-case numerical practice

Try the changed case before feedback

At volume flow 0.003 m³/s, a prescribed irreversible mechanical loss is 4000 Pa. Find dissipated mechanical power in W.

Numerical result in the requested unitsCompare this result

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and limits

Original content checked 30 October 2026 against OpenStax College Physics 2e. All records are supplied or generated educational evidence. No pressure rigs, liquid handling, bodily measurements or physical exposure protocols are requested. Virtual admissibility does not certify real equipment safety, practical skill or independent mastery.