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This is not a homework problem, but an example that was demonstrated that I am confused about. Sorry if it should've been in the other forum nevertheless.

I understand the mathematics of the derivation and the result; but I'm having difficulty reconciling this against common experience with compressed-air hose, garden hose, images of firefighters pushing on an actively discharging hose, etc. I've simplified the example and skipped a few trivial algebraic steps to what is most relevant about my confusion.

Hose of diameter Dh = 0.10m

Nozzle diameter Dn = 0.04m

p(water) = 1000kg/m^3

Taking point 1 to be inside the hose, where the hose diameter is Dh, and point 2 to be just outside the nozzle where pressure is atmospheric, both points at the same z:

continuity:

m1 = m2 = m = 20 kg/s

u1 = 2.55 m/s

u2 = 15.9 m/s

Bernoulli:

P1 = P2 + p/2*(u2^2 - u1^2) = 218 kPa

Drawing a rectangular control volume around the nozzle (see attached), assuming steady-flow (no accumulation of momentum), and assuming that F reqd to hold nozzle stationary is in the same direction as the discharge flow:

Force balance:

P1Ah + F + mu1 = P2Ah + mu2

F = (P2-P1)Ah + m(u2-u1) = -917 N + 259 N = -658 N

The negative force indicates that the force required is against the direction of flow; that is, one must pull on the hose to keep it stationary while it discharges. But how can this be? I've never heard of a nozzle that pulls itself forward in the same direction as the discharge flow. The only self-feeding nozzles I've seen/heard of are ones that have jets pointing backwards (sewer cleaning, etc.) which in of themselves prove my intuition about reality to be true and this example to be flawed somehow.

What am I missing?

I understand the mathematics of the derivation and the result; but I'm having difficulty reconciling this against common experience with compressed-air hose, garden hose, images of firefighters pushing on an actively discharging hose, etc. I've simplified the example and skipped a few trivial algebraic steps to what is most relevant about my confusion.

Hose of diameter Dh = 0.10m

Nozzle diameter Dn = 0.04m

p(water) = 1000kg/m^3

Taking point 1 to be inside the hose, where the hose diameter is Dh, and point 2 to be just outside the nozzle where pressure is atmospheric, both points at the same z:

continuity:

m1 = m2 = m = 20 kg/s

u1 = 2.55 m/s

u2 = 15.9 m/s

Bernoulli:

P1 = P2 + p/2*(u2^2 - u1^2) = 218 kPa

Drawing a rectangular control volume around the nozzle (see attached), assuming steady-flow (no accumulation of momentum), and assuming that F reqd to hold nozzle stationary is in the same direction as the discharge flow:

Force balance:

P1Ah + F + mu1 = P2Ah + mu2

F = (P2-P1)Ah + m(u2-u1) = -917 N + 259 N = -658 N

The negative force indicates that the force required is against the direction of flow; that is, one must pull on the hose to keep it stationary while it discharges. But how can this be? I've never heard of a nozzle that pulls itself forward in the same direction as the discharge flow. The only self-feeding nozzles I've seen/heard of are ones that have jets pointing backwards (sewer cleaning, etc.) which in of themselves prove my intuition about reality to be true and this example to be flawed somehow.

What am I missing?