Question

Water flows at the rate of 3.48 kg/s through a hose with a diameter of 3.00 cm.

(a) What is the speed of water in this hose?


(b) If the hose is attached to a nozzle with a diameter of 0.750 cm, what is the speed of water in the nozzle?



(c) Is the number of kilograms per second flowing through the nozzle greater than, less than, or equal to 3.48 kg/s?

Help! My answers are wrong, heres what I did :(

A) In order to find the speed of the water we are given:

3.48kg/s Water flow
3.00cm diameter (or 1.5cm radius).

Knowing also: dV/dt = AV and dm/dt= p (of water) Av.

Taken together V moves out when dv/dt is substituted dm/dt=p (of water) dV/dt.

V= dm/dt x 1/p (of water)A

Plugging and solving for V. dm/dt = 3.48kg/s. p of water = 1,000kg/m3.

V= 3.48kg/s x 1/ (1,000kg/m3 x A)
V= 3.48kg/s x 1/(1,000kg/m3x pie 1.5^2)
V=3.48kg/s / 1.41
V=2.46m/s

B)

We know that the diameter of the attached hose is .750cm. with the speed of the water from A = 2.46m/s.

A1v1=A2v2
pie r1 v1= pie r2v2
v2=(r1/r2)^2v1

v2= (.015/.00375)^2 x 2.46
V2=39.36m/s

Answer 1

Volume = velocity * area

1kg of water = 1000 cm^3 of water (By definition)

====> 3.48 kg/s = 3,480 cm^3/s

Area = Pi*r^2 = 3.14 * (3/2)^2 = 7.065cm^2

====>

3480 cm^3/s = V * 7.06 cm^2

(3480 cm^3/s) / 7.06 cm^2 = V

a) V= 492.91 cm/s

=4.92m/s

c) Conservation of mass means "equal to"


3480 cm^3/s = V2 * (pi * (0.750/2)^2

3480 cm^3/s = V2 * 0.44 cm^2

b) V2 = 3480/.44= 7909 cm/s=7.9m/s
c) The flow rate is the same everywhere, as water is treated as an incompressible fluid