Question

Water from a leaking tap begins to fall into an empty tank 0.5m wide by 2m long by 4m height .If the drops fall at a rate of 2 drops per second,and if each drops weighs 0.05g .After how many seconds will the pressure at the bottom of the tank be 400Pa.[density of water =1000kg/ms g= 10m/s ]

Answer 1

Find how much water is added per 1 second:

$$m=2·0.05=0.1\text{ g/s, or 0.0001 kg/s}.$$

Next, determine what height of water corresponds to 400 Pa:

$$p=\rho gh, \\\space\\ h=\frac{p}{\rho g}=0.04\text{ m}.$$

Find what volume of water in the tank corresponds to this water level:

$$M=\rho V=\rho wlh=1000·0.5·2·0.04=40\text{ kg }.$$

So, the time is

$$t=\frac Mm=4.6\text{ days}.$$