Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm² and 3 cm² respectively.
The rate of flow will b $e_____cm³·s⁻¹.$ (take g = 10 m·s⁻²)

Question

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm² and 3 cm² respectively.

The rate of flow will b $e_____cm³·s⁻¹.$ (take g = 10 m·s⁻²)

G1 Physics · Accepted Answer

From the continuity equation, A₍ᴀ₎V₍ᴀ₎ = A₍ʙ₎V₍ʙ₎. Therefore, 6V₍ᴀ₎ = 3V₍ʙ₎, so V₍ʙ₎ = 2V₍ᴀ₎. Because the tube is horizontal, Bernoulli's equation gives P₍ᴀ₎ + ½ρV₍ᴀ₎² = P₍ʙ₎ + ½ρV₍ʙ₎². The pressure difference is represented by the 5 cm water-column difference: P₍ᴀ₎-P₍ʙ₎ = ρg(0.05). Hence, ρg(0.05) = ½ρ(V₍ʙ₎²-V₍ᴀ₎²). Using V₍ʙ₎ = 2V₍ᴀ₎, g(0.05) = ½(4V₍ᴀ₎²-V₍ᴀ₎²) = 3V₍ᴀ₎² ───── 2 . Thus, V₍ᴀ₎² = 2g(0.05) ──────── 3 = 1 ─── 3 m²·s⁻². Therefore, V₍ᴀ₎ = 1 ─── √3 m·s⁻¹ = 100 ───── √3 cm·s⁻¹. The vol…

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at A and B are 6 cm² and 3 cm² respectively. The rate of flow will b e_____cm³·s⁻¹. (take g = 10 m·s⁻²)