# Problem: A sump pump is draining a flooded basement at the rate of 0.600 L/s, with an output pressure of 3.00 x 105N/m2. Neglect frictional losses in both parts of this problem.(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 in N/m2?(b) The hose then loses 1.80 m in height from this point as it goes over the foundation wall, and widens to 4.00 cm diameter. What is the pressure now in N/m2?

###### FREE Expert Solution

(a)

Bernoulli's equation:

$\overline{){{\mathbf{P}}}_{{\mathbf{1}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\rho }}{{{\mathbf{v}}}_{{}_{\mathbf{1}}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{\rho }}{\mathbf{g}}{{\mathbf{h}}}_{{\mathbf{1}}}{\mathbf{=}}{{\mathbf{P}}}_{{\mathbf{2}}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\rho }}{{{\mathbf{v}}}_{{\mathbf{2}}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{\rho }}{\mathbf{g}}{{\mathbf{h}}}_{{\mathbf{2}}}}$

Since v1 = v2 and given that the density of water is 1000 kg/m3, we have:

87% (358 ratings)
###### Problem Details

A sump pump is draining a flooded basement at the rate of 0.600 L/s, with an output pressure of 3.00 x 105N/m2. Neglect frictional losses in both parts of this problem.

(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 in N/m2?

(b) The hose then loses 1.80 m in height from this point as it goes over the foundation wall, and widens to 4.00 cm diameter. What is the pressure now in N/m2?