Water is supplied to an office building 30.5 m high through a pipe at ground lev

Question

Water is supplied to an office building 30.5 m high through a pipe at ground level.
(a) Find the minimum pressure in the supplypipe so that water can reach the top floor of the building.
1Pa

(b) Suppose the pressure in the supply pipe is designed so thatwater can flow out through a much smaller pipe on the top floor ata speed of 4.65 m/s. Find the pressure inthe larger pipe on the ground floor.
2Pa (a) Find the minimum pressure in the supplypipe so that water can reach the top floor of the building.
1Pa

(b) Suppose the pressure in the supply pipe is designed so thatwater can flow out through a much smaller pipe on the top floor ata speed of 4.65 m/s. Find the pressure inthe larger pipe on the ground floor.
2Pa

Explanation / Answer

Pressure=F/a F=Vg The total force of gravity pushing down on the water is(30.5meters times area = V)g, density of water is1,000kg/m3 g=9.8m/s2 Pressure=(30.5meters times area = V)g/a =(30.5meters)(1,000kg/m3)(9.8m/s2)=298900Pa orabout 3 atmospheres Bernoulli'sequation:P1+1/2(v1)2+gy1=P2+1/2(v2)2+gy2 P1=P2+1/2(v2)2+gy2-1/2(v1)2-gy1 If we assume that the larger pipe is arbitrarily largecompared to the smaller pipe then the velocity of the flow throughthe larger pipe is arbitrarily zero P1=P2+1/2(v2)2+g(y2-y1) P2=1/2(v2)2=10811Pa 10811Pa+298900Pa=309711Pa Pressure=(30.5meters times area = V)g/a =(30.5meters)(1,000kg/m3)(9.8m/s2)=298900Pa orabout 3 atmospheres Bernoulli'sequation:P1+1/2(v1)2+gy1=P2+1/2(v2)2+gy2 P1=P2+1/2(v2)2+gy2-1/2(v1)2-gy1 If we assume that the larger pipe is arbitrarily largecompared to the smaller pipe then the velocity of the flow throughthe larger pipe is arbitrarily zero P1=P2+1/2(v2)2+g(y2-y1) P2=1/2(v2)2=10811Pa 10811Pa+298900Pa=309711Pa

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