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 0.55 L/s, with an output pressure of 2.9 × 105 N/m2.

a) The water enters a hose with a 3.2 cm inside diameter and rises 2.4 m above the pump. What is its pressure at this point N/m2? You may neglect frictional losses.

Correct answer: 2.7 x 105

b) The hose goes over the foundation wall, losing 0.55 m in height, and widens to 4.9 cm in diameter. What is the pressure now in N/m2? You may neglect frictional losses.

I have tried multiple answers for 'b' and they were all incorrect. Those answers were:
2.96 x 105
2.90 x 105
2.85 x 105

This is my third time asking chegg and I have one more attempt! Please help.

Explanation / Answer

Here ,

at the hose , initial speed of water flow , v1

v1 * A1 = V

v1 * pi * (0.016)^2 = 0.55 *10^-3

v1 = 0.684 m/s

now , for the hose at the foundation ,

speed of flow is v2

v2 * pi * (0.049/2)^2 = 0.55 *10^-3

v2 = 0.292 m/s

Now , for the final pressure ,

P2 = P1 + p * g * h + 0.5 * p * (v1^2 - v2^2)

P2 = 2.7 *10^5 + 1000 * 9.8 * 0.55 + 0.5 *1000 *(0.684^2 - 0.292^2)

P2 = 2.755 *10^5 Pa

the pressure at the hose now is 2.755 *10^5 Pa

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