Gauge pressure in water hose behind nozzle with tank and stopper

[amcca064]

A village maintains a large tank with an open top, containing water for emergencies. The water can drain from the tank through a hose of diameter 6.60cm. the hose ends with a nozzle of diameter 2.20 cm. A rubber stopper is inserted into the nozzle. the water level in the tank is kept 7.50 m above the nozzle. a) Calculate the friction force exerted on the stopper by the nozzle. b) the stopper is removed. What mass of water flows from the nozzle in 2.00hours? c)Calculate the Gauge pressure of the flowin water in the hose just behind the nozzle.

Ok so part a I did by using Bernoulli's Equation, finding pressure by assuming the pressure at a point on the waters surface at the top of the tank to be atmospheric, and that the pressure at the nozzle is some pressure P + atmospheric pressure, atmospheric pressure cancels, and resulting pressure is just density H20 X g X 7.50m = 73600 Pa. Sound good so far?

Part b i did by saying pressure is F/A so F=P X A, after finding the area of the nozzle. Then that force has to equal the friction force because we assume the stopper not to be moving (equilibrium), (also assume stopper has same area as nozzle). turned out to be -28.0N. Is that OK too??

Then part c has me stuck, what is gauge pressure exactly? and how do you find it for this situation, I read in my text that it is the absolute pressure minus the atmoshperic pressure? so in this case would it be 73600-101300? because that doesn't make much sense, or did I find the gauge pressure already??

 

[amcca064]

Help please! anybody...

 

[Andrew Mason]

...Then part c has me stuck, what is gauge pressure exactly? and how do you find it for this situation, I read in my text that it is the absolute pressure minus the atmoshperic pressure? so in this case would it be 73600-101300? because that doesn't make much sense, or did I find the gauge pressure already??

Absolute pressure at a depth in the tank is atmospheric pressure + pressure from water in the tank (the latter being the gauge pressure). You have found the the gauge pressure in the tank in a). The gauge pressure in the hose is what you want to find.

You want to analyse the water in each of the three locations: 1) in the tank 2) in the hose 3) in the air after it passes through the nozzle. The pressure in 3) of course is atmospheric pressure. The pressure in the tank at depth h is atmospheric pressure + $\rho g h$.

You are asked to find the difference between the pressure in the hose and the pressure outside. In order to do that you need first to determine the speed of the flow outside nozzle. That will give you the rate of mass flow (b). You find that from Bernoulli's equation. From that you can determine the speed in hose. Apply Bernoulli's equation at that position to find the pressure. Then subtract atmospheric pressure to find the gauge pressure.

AM