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(a) What is the pressure drop due to the Bernoulli effect

Chapter 12, Problem 23

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QUESTION:

(a) 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.)

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QUESTION:

(a) 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.)

ANSWER:

Step 1 of 4

Here we have to find the pressure drop and the maximum height above the nozzle which the water can reach.

The diameter of the 1st nozzle is, \(D_{1}=3 \mathrm{~cm}=0.03 \mathrm{~m}\).

So, the radius will be, \(r_{1}=1.5 \mathrm{~cm}=0.015 \mathrm{~m}\).

The diameter of the fire hose is, \(D_{2}=9 \mathrm{~cm}=0.09 \mathrm{~m}\).

So, the radius is \(r_{2}=4.5 \mathrm{~cm}=0.045 \mathrm{~m}\).

The volume flow inside the fire hose is,

\(\dot{V}=40 L / s\)

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