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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 0.750 L/s, with an output pressure of 3.00×105N/m23.00×105N/m2. (a) The water enters a hose with a 3.00-cm inside diameter and rises 2.50 m above the pump. What is its 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.

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 0.750 L/s, with an output pressure of 3.00×105N/m23.00×105N/m2. (a) The water enters a hose with a 3.00-cm inside diameter and rises 2.50 m above the pump. What is its 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.

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. 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 0.750 L/s, with an output pressure of 3.00×105N/m23.00×105N/m2. (a) The water enters a hose with a 3.00-cm inside diameter and rises 2.50 m above the pump. What is its 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.

Expert Solution
Step 1: Bernoulli's theorem

Given,

The output pressure, P subscript 1 equals 3 cross times 10 to the power of 5 N divided by m squared

Rate of water flow, Q equals 0.75 space L divided by s Q equals 0.75 cross times 10 to the power of negative 3 end exponent m cubed divided by s

The height, increment h equals 2.5 m

Diameter, d equals 3 c m d equals 0.03 m

According to Bernoulli's theorem,

The density of the water, rho equals 1000 k g divided by m cubed

The velocity is constant.

P subscript 1 plus rho subscript 1 g h subscript 1 plus 1 half rho subscript 1 v subscript 1 superscript 2 equals P subscript 2 plus rho subscript 2 g h subscript 2 plus 1 half rho subscript 2 v subscript 2 superscript 2 v subscript 1 tilde v subscript 2 equals 0 rho subscript 1 equals rho subscript 2 equals rho h subscript 1 minus h subscript 2 equals increment h P subscript 1 plus rho g h subscript 1 equals P subscript 2 plus rho g h subscript 2 P subscript 2 equals P subscript 1 plus rho g increment h P subscript 2 equals 3 cross times 10 to the power of 5 plus 1000 cross times 9.8 cross times 2.5 P subscript 2 equals 3.245 cross times 10 to the power of 5 N divided by m squared

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