# Pumps

Pump that draws water at velocity 3.5 liters per second water from a construction trench take 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 is the pumping velocity would have had to pump that water from the trench after a maximum 25 minutes?

Correct result:

t2 =  16.55 min
v3 =  4.9 l/s

#### Solution:

$Q = v_1 t_1 = v_2 t_2 \ \\ \ \\ t_2 = \dfrac{ v_1 }{ v_2} t_1 = \dfrac{ 3.5 }{ 7.4} \cdot 35 = 16.55 \ \text{min} \ \\$
$v_1 t_1 = v_3 t_3 \ \\ \ \\ v_3 = v_1 \cdot \dfrac{ t_1 }{ t_3 } = 3.5 \cdot \dfrac{ 35 }{ 25} \ \\ v_3 = 4.9 \ \text{l/s}$

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