Question

boat can safely displace 2.50 m3 of water without sinking, and the boat itself has a mass of 850 kg. What maximum mass of passengers and cargo can the boat carry safely in a fresh-water lake? [6] 2.2 A pipe in the basement of an apartment complex is accidentally punctured, causing a leak through the small hole formed (see Figure 2). An astute physics student estimates that the water is leaking out a speed of 25 m/s. Apply the Bernouli equation to estimate the gauge pressure inside the pipe. [8]

Answer 1

1) The buoyancy force acting upward on the boat:

$$F_B=\rho g V.$$

Unless downward force equal to the buoyancy in magnitude is achieved, the boat with passengers can float safely:

$$(m_{boat}+m_{pass})g=\rho g V,$$

$$m_{pass}=\rho V-m_{boat}=1000\cdot2.5-850=1650\text{ kg}.$$

2) According to Bernoulli's equation:

$$0.5\rho v^2=p_a+p_g,$$

$$p_g=\frac{\rho v^2}{2}-p_a=\frac{1000\cdot25^2}{2}-101325=211175\text{ Pa}.$$