Question

Question 4 Two boats are traveling parallel at speed 7.0 m/s in a freshwater lake. But the water between them is accelerated to 9.0 m/s. What is the pressure difference across the width of each boat? v large n Pol

Answer 1

What is the pressure difference across the width of each boat?

According to Bernoulli's theorem, we have

P_A + (1/2) _{$\rho$ w} v_A² = P_B + (1/2) _{$\rho$ w} v_B²

(P_A - P_B) = (1/2) _{$\rho$ w} v_B² - (1/2) _{$\rho$ w} v_A²

$\Delta$P = (1/2) _{$\rho$ w} (v_B² - v_A²)

where, _{$\rho$ w} = density of fresh water = 1030 kg/m³

v_B = speed of a boat B = 9 m/s

v_A = speed of a boat A = 7 m/s

then, we get

$\Delta$P = (0.5) (1030 kg/m³) [(9 m/s)² - (7 m/s)²]

$\Delta$P = (515 kg/m³) (32 m²/s²)

$\Delta$P = 16480 Pa