Problem: A sump pump (used to drain water from the basement of houses built below the water table) is draining flooded basement at a rate of 0.750 L/s, with an output pressure of 3.00x105 N/m2.(a) The water enters a hose with a 3.00-cm inside diameter and rises 2.50 m above thew pump. What is the pressure at this point?(b) the hose goes over the foundation wall, losing 0.500 m in height, and widens to 4.00 cm in diameter. what is the pressure now? You may neglect frictional losses in both parts of the problem.

FREE Expert Solution

From Bernoulli's principle:

P1+12ρ1v12+ρ1h1g=P2+12ρ2v22+ρ2h2g=constant

(a)

Since it has the same velocity, the equation is reduced to:

P1+ρ1h1g=P2+ρ2h2g

P2 is obtained as:

P2=P1+ρ1h1g-ρ2h2g=P1+ρg(h)=3.00×105+(1×103)(9.8)(2.50)

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Problem Details

A sump pump (used to drain water from the basement of houses built below the water table) is draining flooded basement at a rate of 0.750 L/s, with an output pressure of 3.00x105 N/m2.

(a) The water enters a hose with a 3.00-cm inside diameter and rises 2.50 m above thew pump. What is the pressure at this point?

(b) the hose goes over the foundation wall, losing 0.500 m in height, and widens to 4.00 cm in diameter. what is the pressure now? You may neglect frictional losses in both parts of the problem.