Problem 28PE

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 3.00×105 N/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.

Solution to 28PE

Step 1 of 5

We are asked to compute the pressure at above the pump and in the next part we have to find the pressure if the diameter of hose increases.

We have to use bernoulli’s equation and continuity equation to solve this problem.

Bernoulli’s equation,

Where,

is the pressure.

is the velocity

is the density of the fluid.

is the acceleration due to gravity

is the height

Equation of continuity,

Here,

is the velocity of the fluid,

is the cross-sectional area of the pipe.