Question

Water circulates throughout a house in a hot-water heating system. If the water is pumped at a speed of 0.50 m/s through a 4.0-cm-diameter pipe in the basement under a pressure of 3.0 atm, what will be the flow speed and pressure in a 2.6-cm-diameter pipe on the second floor 5.0 m above? Assume the pipes do not divide into branches. (15 pts)

Answer 1

Answer:

The flow speed at 2.6 cm diameter pipe is 1.2 $\frac{m}{s}$

Explanation:

Given :

Speed at 4 cm diameter pipe $v_{1} = 0.50 \frac{m}{s}$

Area of 4 cm diameter pipe $A_{1} = \pi (2 \times 10^{-2} )^{2}$

$A_{1} = 12.56 \times 10^{-4}$$m^{2}$

Area of 2.6 cm diameter pipe $A_{2} = \pi (1.3 \times 10^{-2} )^{2}$

$A_{2} = 5.306 \times 10^{-4} m^{2}$

From the equation of continuity,

   $A_{1} v_{1} = A_{2} v_{2}$

Find the speed at 2.6 cm diameter pipe,

      $v_{2} = \frac{A_{1} v_{1} }{A_{2} }$

      $v_{2} = \frac{12.56 \times 10^{-4} \times 0.50 }{5.306 \times 10^{-4} }$

      $v_{2} =1.2 \frac{m}{s}$

Therefore, the flow speed at 2.6 cm diameter pipe is 1.2 $\frac{m}{s}$