What is the pressure drop (due to the bernoulli effect) as water goes into a 3.00 cm diameter nozzle from a 9.00 cm diameter fire hose while carrying a flow of 40.0 l/s? (b) to what maximum height above the nozzle can this water rise? (the actual height will be significantly smaller due to air resistance.)

1581357.68216 Pa

163.21352 m

Explanation:

A = Area =

v = Velocity

1 denotes inlet

2 denotes exit

= Density of water = 1000 kg/m³

Flow rate is given by

From the Bernoulli equation we get

The pressure drop is 1581357.68216 Pa

From the Bernoulli equation

The height is 163.21352 m

(a) 1581935 Pa

(b) 161.4 m

Explanation:

diameter, d = 3 cm

r = 1.5 cm

diameter, d = 9 cm

R = 4.5 cm

Volume per second, V = 40 L/s = 0.04 m^3/s

V = a x v1

0.04 = 3.14 x 0.015 x 0.015 x v1

v1 = 56.6 m/s

Now, 0.04 = 3.14 x 0.045 x 0.045 x v2

v2 = 6.3 m/s

(a) By use of Bernoullie's theorem

where, d be the density of water

P2 - P1 = 1581935 Pa

(b) Let h be the maximum height

P2 - P1 =  x d x g

1581935 = h x 1000 x 9.8

h = 161.4 m

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