Show your work and include units with your answers for full credit A fire depart

Question

Show your work and include units with your answers for full credit A fire department's tanker truck can hold 10 m3 of water (10,000 L. or about 2500 gallons). When in use, the truck forces water through a hose and out of a 3.0-cm-diametcr nozzle with a nf R.50 m/s. I Use Bernoulli's equation to find the absolute pressure inside the tank. Assume the speed of the w ater inside the tank is zero. How long will it take to empty the tank at this rate? Assume the pressure inside the tank is kept constant. Give your answer in seconds and in minutes.

Explanation / Answer

volume of water, v=10 m^3

diameter of the nozzle,d=3cm

radius of the nozzle, r=1.5cm

cross-sectionla area. a=pi*r^2

efflex speed v=8.5 m/sec

v=sqrt(2gh)

8.5=sqrt(2*9.8*h)

==> h=3.686 m

depth of the orifice, h=3.686 m

a)

from the Bernoulli's equation,

P+(1/2*rho*v^2)+(rho*g*h)=constant

=====>

P1+(1/2*rho*v1^2)+rho*g*h1=P2+(1/2*rho*v2^2)+rho*g*h2

P1+(1/2*rho*v1^2)=P2+(1/2*rho*v2^2)

==>

P1-P2=1/2*rho*(v1^-v2^2)

P1-Po=1/2*1000*(8.5^2-0)

P1=Po+36125 pascal

P1=1.013*10^5+36125

P1=1.37*10^5 pascal

b)

time taken to empty the tank,

t=(2*A/a)*sqrt(h/2*g)

t=(2*A*h/a*h)*sqrt(h/2*g)

t=(2*V/a*h)*sqrt(h/2*g)

t=2*10/(pi*(0.015))^2*sqrt(3.686/(2*9.8))

t=3905.686 sec

t=65.1 min

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