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  • Water enters a house through a pipe with inlet diameter of 2.0 cm at an absolute pressure of 4.0 × 105 Pa (about 4 atm). A 1.0 cm diameter pipe leads to the second floor bathr

Water enters a house through a pipe with inlet diameter of 2.0 cm at an absolute pressure of 4.0 × 105 Pa (about 4 atm). A 1.0 cm diameter pipe leads to the second floor bathroom 5.0 m above. When flow speed at the inlet pipe is 1.5 m/s, What will be the flow speed, pressure and volume flow rate in the bathroom respectively - 

Option: 1

6 m/s , 6.6 \times 10^5 Pa, 4.7 \times 10^{-4} m^3/s


Option: 2

3 m/s , 3.3 \times 10^5 Pa, 5.7 \times 10^{-4} m^3/s


Option: 3

4 m/s , 4 \times 10^5 Pa, 3.2 \times 10^{-4} m^3/s


Option: 4

6 m/s , 3.3 \times 10^5 Pa, 4.7 \times 10^{-4} m^3/s


Answers (1)

best_answer 
Let points 1 and 2 be at the inlet pipe and at the bathroom, then from continuity equation,

                                a_1v_1 = a_2v_2 \\ \Rightarrow v_2 = 6.0 m/s

Now, applying Bernoulli's equation at the inlet (y = 0) and at the bathroom (y2 = 5.0 m).

As, P + \frac{1}{2} \rho v^2 + \rho gy = constant

Hence, P_2 = P_1 - 1/2 \rho (v^2_2-v^2_1 ) - \rho g(y_2-y_1 )

which gives P_2 = 3.3 \times 10^5 Pa

The volume flow rate = A2v2 = A1v1 =  \dpi{100} \frac{\pi}{4} (0.01)^2 \times 6  = 4.7 \times 10^{-4} m^3/s.

 

Posted by

Pankaj Sanodiya

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