Water flows through a water hose at a rate of V 1 = 780 cm 3 /s, the diameter of

Question

Water flows through a water hose at a rate of V1 = 780 cm3/s, the diameter of the hose is d1 = 2.27 cm. A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of v2 = 14.4 m/s.

Randomized VariablesV1 = 780 cm3/s
d1 = 2.27 cm
v2 = 14.4 m/s (a) Express the cross-sectional area of the hose, A1, in terms of d1.
(b) Calculate the numerical value of A1 in cm2.
(c) Express the speed of the water inside the hose, v1, in terms of V1 and A1.
(d) Calculate the numerical value of v1 in m/s.
(e) Express the cross-sectional area of the nozzle, A2, in terms of v1, v2 and A1. (f) Calculate the numerical value of A2 in cm2 Water flows through a water hose at a rate of V1 = 780 cm3/s, the diameter of the hose is d1 = 2.27 cm. A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of v2 = 14.4 m/s.

Randomized VariablesV1 = 780 cm3/s
d1 = 2.27 cm
v2 = 14.4 m/s (a) Express the cross-sectional area of the hose, A1, in terms of d1.
(b) Calculate the numerical value of A1 in cm2.
(c) Express the speed of the water inside the hose, v1, in terms of V1 and A1.
(d) Calculate the numerical value of v1 in m/s.
(e) Express the cross-sectional area of the nozzle, A2, in terms of v1, v2 and A1. (f) Calculate the numerical value of A2 in cm2

Explanation / Answer

(a)

A1 = (/4)*(d1)^2

(b)

A1 = (/4)*(2.27)^2

=4.047 cm2

(c)

v1= V1/A1

(d)

v1= 780/4.047

v1=192.73 cm/ s /100 = 1.9273 m/s

(e)

V1 = A2v2

A2 = V1/v2

A2 = (A1*v1) / v2

(f)

A2 = (A1*v1) / v2

A2 = (4.047*1.9273)/14.4

A2= .54156 cm2

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