Question
Water flows at 2.4 m/s through a garden hose of diameter 1.59 cm and emerges from a nozzle of
radius 0.64 cm. If the nozzle is directed vertically upward, to what height would the water rise?
radius 0.64 cm. If the nozzle is directed vertically upward, to what height would the water rise?
Answers
Damon
all you need to know is the speed of a hunk of water headed up.
Q = flow rate = hose area * v
Q = pi (.0159)^2 /4 * 2.4
Q = .000477 m^3/second
but
Q = flow rate = nozzle area * speed
Vi = initial speed up
.000477 m/s = pi r^2 Vi
.000477 = pi (.0064)^2 Vi
Vi = 3.7 m/s
Now we have a plain old throw it straight up problem with initial speed up of 3.7 m/s
v = Vi - 9.81 t
v = 0 at top
t = .373 seconds rising
then
h = 4.9 t^2
h = .68 meters
Q = flow rate = hose area * v
Q = pi (.0159)^2 /4 * 2.4
Q = .000477 m^3/second
but
Q = flow rate = nozzle area * speed
Vi = initial speed up
.000477 m/s = pi r^2 Vi
.000477 = pi (.0064)^2 Vi
Vi = 3.7 m/s
Now we have a plain old throw it straight up problem with initial speed up of 3.7 m/s
v = Vi - 9.81 t
v = 0 at top
t = .373 seconds rising
then
h = 4.9 t^2
h = .68 meters