First select a control volume to include the hose, nozzle and
water inside the hose, as shown by the red dashed lines in the figure.
Rx and Ry represent the reaction force components
acting on the hose. W is the weight of the water inside the hose.
The linear momentum equation for steady flow is given by
which can be written in terms of x- and y- component as follows:
p2A2cos45o + Rx
= V1ρ(-V1)A1 + V2cos45oρ(V2)A2
- p2A2sin45o - W +
Ry = V2sin45oρ(V2)A2
gage pressure at the nozzle outlet is zero (i.e., p2 =
0) since water is discharged to the atmosphere. According to the principle
conservation of mass,
The linear momentum equations can be simplified to yield the reaction
force in the x- direction: