A sump pump (used to drain water from the basement of houses built below the wat

Question

A sump pump (used to drain water from the basement of houses built below the water table) is draining a flooded basement at the rate of 0.75 L/s, with an output pressure of 2.85 × 105 N/m2.

a)The water enters a hose with a 3.1 cm inside diameter and rises 2.8 m above the pump. What is its pressure at this point N/m2? You may neglect frictional losses.

Answer is 257600

I need answer to part B

b) The hose goes over the foundation wall, losing 0.65 m in height, and widens to 4.8 cm in diameter. What is the pressure now in N/m2? You may neglect frictional losses.

Explanation / Answer

from equation of continuity

flow rate = A1*v1 = A2*v2

v1 = 0.75*10^-3/(pi*0.0155^2) = 0.994 m/s

v2 = 0.75*10^-3/(pi*0.024^2) = 0.414 m/s^2

P1 + 0.5*rho*v1^2 + rho*g*h1 = P2 + 0.5*rho*v2^2 + rho*g*h2

(2.85*10^5)+(0.5*1000*0.994^2) + 0 = (P2)+(0.5*1000*0.414^2) + (1000*9.8*(2.8+0.65))

P2 = 251598.3 N/m^2

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