A house at the bottom of a hill is fed by a full tank of water h = 5.50 m deep a

Question

A house at the bottom of a hill is fed by a full tank of water h = 5.50 m deep and connected to the house by a pipe that is d = 150 m long at an angle of theta = 53.0 degree from the horizontal. (Figure 1) Determine the water gauge pressure at the house. Express your answer to three significant figures and include the appropriate units. How high could the water shoot if it came vertically out of a broken pipe in front of the house? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

A ) The guage pressure at the bottom of the house Pg=hdg where h=5.50+150sin530=125 m and d is the density of the water=1000kg/m3

Therefore Pg=1.23*106Pa.

B) By applying Bernoulli's principle we can obtain the velocity of the water at the bottom of the house

i.e. p1+0+dgy1=p2+1/2dv22+dgy2

Therefore 1/2dv22=(p1-p2)+dg(y1-y2)=2dgh

i.e. v22=4dgh

Applying the same principle we can obtain the height to which the water shoots out of a vertical broken pipe

i.e. p2+1/2dv22+dgy2=p3+dgy3

i.e. p2+2dgh=dg(y3-y2)

If h3=y3-y2 and substituting the value of h=550+150sin530=125 m

we obtain the value of h3=(p2+2dgh)/dg=125+2h=125+250=375 m

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