Basements that are prone to flooding are generally equipped with a sump pump, as illustrated in the image. (For purposes of illustration, the house above the basement has been removed, and dimensions have been distorted.) Water is diverted from the foundation, or wherever it seeps into the basement, to a small well in the floor. When needed, the submerged pump automatically switches on, pumping the water a height H above the pump through a pipe with diameter d. The pipe carries the water over the basement wall where it loses height hℎ and connects to a wider pipe, with diameter D, parallel to the ground. (Note the use of both lower-case and upper-case letters.) When the pump is operating, the flow rate is 0.574L/s with an output pressure of 1.27×105Pa. a. The water enters the pipe with an inside diameter d=2.58cm and rises to a maximum height H=2.44m above the pump. What is the pressure, in pascals, at the maximum height? (Neglect frictional losses.) b. The pipe carries the water over the basement wall where it loses h=0.71m in height and widens to a diameter of D=7.21cm. What is the pressure, in pascals, in the wider pipe? (Neglect frictional losses.)
Basements that are prone to flooding are generally equipped with a sump pump, as illustrated in the image. (For purposes of illustration, the house above the basement has been removed, and dimensions have been distorted.) Water is diverted from the foundation, or wherever it seeps into the basement, to a small well in the floor. When needed, the submerged pump automatically switches on, pumping the water a height H above the pump through a pipe with diameter d. The pipe carries the water over the basement wall where it loses height hℎ and connects to a wider pipe, with diameter D, parallel to the ground. (Note the use of both lower-case and upper-case letters.) When the pump is operating, the flow rate is 0.574L/s with an output pressure of 1.27×105Pa.
a. The water enters the pipe with an inside diameter d=2.58cm and rises to a maximum height H=2.44m above the pump. What is the pressure, in pascals, at the maximum height? (Neglect frictional losses.)
b. The pipe carries the water over the basement wall where it loses h=0.71m in height and widens to a diameter of D=7.21cm. What is the pressure, in pascals, in the wider pipe? (Neglect frictional losses.)
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