Question

In your kitchen, the sink is 60 cm by 45.7 cm. by 30.5 cm. deep. You are filling it with water at the rate of 252 × 10−6 m3 /s. How long will it take (in min) to half fill the sink?After this you turn off the faucet and open the drain slightly so that the tank starts to drain at 63×10−6 m3 /s. What is the rate (m/s) at which the water level drops?

Answer 1

Answer:

3.326.10^-3

Explanation:

given data

a=60 cm=0.06m

b=45.7 cm=0.0457m

h=30.5 cm=0.0305m

first we have to find the volume:

V=a.b.c

V=0.06×0.0457×0.0305

V=0.083$m^{3}$

$V_{half}$=$\frac{V}{2}$

$V_{half}$=0.041$m^{3}$

The volume flow represent the ratio of volume to time:

$Q=\frac{V}{t}$

$t=\frac{V}{Q}$

$Q=252.10^{-6}m^{3} /s$

$t=\frac{0.041}{252.10^{-6} }$

$t=16269.84s$

$t=271.16 min$

to determine the water level drops

$t=\frac{V}{Q}$

$Q=63.10^{-6} m^{3} /s$

$t=\frac{0.041}{63.10^{-6} }$

$t=6721.31s$

now we have to determine water level in sink

$h=\frac{V}{a.b}$

  =$\frac{0.041}{0.06.0.457}$

  =0.149 m

now we have to find the ratio m/s

$\frac{h}{t}=\frac{0.149}{6721.31}\\ \\ \frac{h}{t}=3.326.10^{-3} m/s$