$\text {Water, issuing from an 8-mm-diameter nozzle, impacts the blade}$ $\text {with a velocity $V _ { 1 } = 50 \mathrm {~m} / \mathrm { s }$, as shown. The $x$-component of the }$$\text {force of the water on the blade is nearest}$

Question

Quizplus · Accepted Answer

$198 \mathrm {~N}$
$\text {The velocity of the water as it moves over the blade}$ $\text {remains at $50 \mathrm {~m} / \mathrm { s }$ since the pressure remains constant and}$ $\text {there is negligible elevation change. We ignore any slight}$ $\text {slowing of the water due to friction. Apply the}$ $\text {momentum equation (4.6.6):}$
$$\begin{aligned}
R _ { x } = \dot { m } \left( V _ { 2 x } - V _ { 1 x } \right) & = \left[ 1000 \times \left( \pi \times 0.004 ^ { 2 } \right) \times 50 \right] \left( - 50 \cos 30 ^ { \circ } - 50 \cos 45 ^ { \circ } \right) \
& = - 198 \mathrm {~N}
\end{aligned}$$
The force component above represents the action of the blade on the water. The force of the water on the blade would be $ 198 \mathrm{~N} $.

Water, issuing from an 8-mm-diameter nozzle, impacts the blade\text {Water, issuing from an 8-mm-diameter nozzle, impacts the blade}Water, issuing from an 8-mm-diameter nozzle, impacts the blade

$\text {Water, issuing from an 8-mm-diameter nozzle, impacts the blade}$