Question

A nozzle with a radius of .33 cm is attached to a garden hose with a radius of .85 cm. the flow rate through hose and nozzle is .55 L/s.

a. Calculate the maximum height to which water could be squirted with the hose if it emerges from the nozzle in m.

b. Calculate the maximum height (in cm) to which water could be squirted with the hose if it emerges with the nozzle removed, assuming the same flow rate.

Answer 1

1)we have the formula for density as

density = mass / volume------(1)

= m /v

v = 4/3r^3

substituting in eqn (1) we have

1000 = m / (4/3 x3.14)(0.33x10^-2)^3

= 1000kg/m3

we have m = 1.49x10^-4kg

pressure P = gh--------(2)

but pressure P = F / A------(3)

F = mg = (1.49x10^-4)(9.8)

F = 1.46x10^-3N

AREA A = r^2

      =(3.14)(0.33x10^-2)^2

A = 3.41x10^-5 m^2

substituting in eqn (3) we have

P = 1.46x10^-3 / 3.41x10^-5

P = 42.81Pa

from eqn (2) we have

height h = P / g

          =42.81 / (1000)(9.8)

h = 4.38x10^-3m

2) for the second part r = 0.85cm

following the same procedures we have

mass m = 2.56kg

pressure P = 110.97x10^3Pa

area A = 2.26x10^-4m^2

force F = 25.08 N

SUBSTITUTING IN THE EQUATION WE HAVE THE HEIGHT

h = P / g

   = 0.1132cm