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Igoryamba
2 years ago
12

A garden hose with a diameter of 0.64 in has water flowing in it with a speed of 0.46 m/s and a pressure of 1.9 atmospheres. At

the end of the hose is a nozzle with a diameter of 0.25 in.(a) Find the speed of water in the nozzle.(b) Find the pressure in the nozzle.
Physics
1 answer:
STALIN [3.7K]2 years ago
7 0

Answer:

(a).The speed of the water in the nozzle is 3.014 m/s.

(b). The pressure in the nozzle is 1.86 atm.

Explanation:

Given that,

Nozzle diameter = 0.25 in = 0.00635 m

Hose pipe diameter = 0.64 in = 0.016256 m

Pressure = 1.9 atm =192518 Pa

(a). We need to calculate the speed of the water in the nozzle

Flow Speed at the inlet pipe will be given by using Continuity Equation

Q_{1}=Q_{2}

v_{1}A_{1}=v_{2}A_{2}

v_{1}=v_{2}\times(\dfrac{A_{2}}{A_{1}})

Where, A = area of pipe

A=\pi\times \dfrac{d^2}{4}

v_{1}=v_{2}\times(\dfrac{d_{2}^2}{d_{1}^2})

Put the value into the formula

v_{1}=0.46\times\dfrac{(0.016256)^2}{(0.00635)^2}

v_{1}=3.014\ m/s

The speed of the water in the nozzle is 3.014 m/s.

(b). We need to calculate the pressure in the nozzle

Using Bernoulli's Theorem,

P_{1}+\dfrac{1}{2}\rho\times v_{1}^2+\rho gh_{1}=P_{2}+\dfrac{1}{2}\rho\times v_{2}^2+\rho gh_{2}

Where, h_{1}=h_{2}

P_{1}+\dfrac{1}{2}\rho\times v_{1}^2=P_{2}+\dfrac{1}{2}\rho\times v_{2}^2

P_{1}=P_{2}+\dfrac{1}{2}\rho(v_{2}^2-v_{1}^2)

Put the value into the formula

P_{1}=192518 +\dfrac{1}{2}\times1000\times((0.46)^2-(3.014)^2)

P_{1}=188081.702\ Pa

P=1.86\ atm

Hence, (a).The speed of the water in the nozzle is 3.014 m/s.

(b). The pressure in the nozzle is 1.86 atm.

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