Pumps

Pump drawing water at velocity 3.5 liters per second from a construction trench takes 35 minutes.

a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second.
b) What pumping velocity would you have had to pump that water from the trench after a maximum of 25 minutes?

Correct answer:

t₂ =  16.55 min
v₃ =  4.9 l/s

Step-by-step explanation:

$$\begin{gathered} v_1=3.5\text{l/s} \\ {t}_1=35\text{min}\to \text{s}=35\cdot 60\text{s}=2100\text{s} \\ {v}_2=7.4\text{l/s} \\ Q=v_1{t}_1=v_2{t}_2 \\ {T}_2=\frac{v_1\cdot t_1}{v_2}=\frac{3.5\cdot 2100}{7.4}=\frac{36750}{37}\doteq 993.2432\text{s} \\ {t}_2=T_2\to \text{min}=T_2:60\text{min}=993.2432:60\text{min}=16.55\text{min}=16.55\text{min} \end{gathered}$$

$$\begin{gathered} t_3=25\text{min}\to \text{s}=25\cdot 60\text{s}=1500\text{s} \\ {v}_1{t}_1=v_3{t}_3 \\ {v}_3=\frac{v_1\cdot t_1}{t_3}=\frac{3.5\cdot 2100}{1500}=4.9\text{l/s} \end{gathered}$$

Try another example