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.
1 Pa

(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.
2 Pa (a) Find the minimum pressure in the supplypipe so that water can reach the top floor of the building.
1 Pa

(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.
2 Pa

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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