Water flows in a horizontal tube as shown in figure below. The pressure of water changes by 600 N/m² between A and B where the area of cross section is 30cm² and 15 cm² respectively. Calculate the rate of flow of water through the tube.

Question:
Water flows in a horizontal tube as shown in figure below. The pressure of water changes by 600 N/m² between A and B where the area of cross section is 30cm² and 15 cm² respectively. Calculate the rate of flow of water through the tube.

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Solution:

Let V_a and V_b be the velocity of water flowing in the tube at point A and B respectively.

By the equation of continuity,

$\frac{{{v_a}}}{{{v_b}}} = \frac{{15}}{{30}} = 0.5$

Or, $V_a$=$\frac{1}{2}$$V_b$

From Bernoulli’s Theorem:

P_a+$\frac{1}{2}$ρv_a² = P_b +$\frac{1}{2}$ρv_b²

or, P_a – P_b = $\frac{1}{2}$ρ[v_b²- v_a²]

or, P_a – P_b =$\frac{1}{2}$ ρ [{2v_a}²  - v_a²]

or, 600 = $\frac{1}{2}$ ×1000× 3v_a²

or, v_a² =0.4  

or, V_a = 0.63

Thus, the velocity of water flowing through tube is 0.6324m/s.