Question

Your uncle is in the below-deck galley of his boat while you are spear fishing in the water nearby. An errant spear makes a small hole in the boat’s hull, and water starts to leak into the galley. (a) If the hole is 0.09 m below the water surface and has area 1.20 cm², how long does it take 10.0 L of water to leak into the boat? (b) Do you need to take into consideration the fact that the boat sinks lower into the water as water leaks in?

Short answer

Answer

1. The time taken to 10.0 L water leak into the boat is, 19.8 s.
2. No need to take the consideration of boat sink.

Step-by-step solution

Step-by-Step Solution Step 1: Identification of the given data

The given data can be listed below as,

• The hole below the water surface is, h₂= h= 0.900m .
• The area of the hole is, A=1.320 cm² .
• The amount of water is, V = 10.0 L .

Significance of Bernoulli’s equation

The total energy per unit mass of a fluid flowing, i.e., the sum of the fluid's kinetic energy, potential energy, and pressure energy at any point in its interior is equal to a constant value.

Determination of the time taken to 10.0 L water leak into the boat

Part (a)

The pressure at the top of the water is equal to the atmospheric pressure and speed of water at the surface is zero (1m³ = 1000L) . The Bernoulli’s equation is expressed as,

$p_1+\frac{1}{2}\rho v_1^2+\rho g{h}_1=p_2+\frac{1}{2}\rho v_2^2+\rho g{h}_2$

Here, ${\rho }_{1}and{\rho }_2$are the pressure at the top and bottom level of the water surface, and h₁ and h₂ are the heights of the top and bottom level of the water surface, $\rho$is the density of water, and g is the gravitational acceleration.

Substitute all the value in the above equation.