Question

A mixing tank initially contains 2000 lb of liquid water. The tank has two inlet pipes, one delivering hot water at a mass flow rate of 0.8 lb/s and the other delivering cold water at a mass flow rate of 1.2 lb/s. Water exits through a single exit pipe at a mass flow rate of 2.5 lb/s. Determine the amount of water, in lb, in the tank after 40 minutes.

Answer 1

Answer:

The  total amount is  $T = 800 \ lb$

Explanation:

from the question we are told that

    The  initial mas of water in the tank is  $m_i = 2000\ lb$

     The mass flow rate of the hot water  inlet pipe is  $\r m_h = 0.8 \ lb/s$

    The mass flow rate of the cold  water  inlet pipe is $\r m_c = 1.2 \ lb/s$

    The mass flow rate  of the exit pipe is $\r m_l = 2.5 \ lb/s$

     The  time being considered is $t = 40\ minutes = 40 * 60 = 2400 \ s$

The amount of water deposited by the hot inlet pipe in 40 minutes is mathematically represented as

       $A_h = m_h * t$

substituting values

       $A_h = 1.2 * 2400$

       $A_h = 1920 \ lb$

The amount of water deposited by the cold  inlet pipe in 40 minutes is mathematically represented as

     $A_c = m_c * t$

substituting values

    $A_c = 1.2 * 2400$

    $A_c = 2880 \ lb$

The total amount of water that let the tank after 40 \minutes is

     $L = \r m_l * t$

substituting values

    $L = 2.5 * 2400$

    $L = 6000$

The  total amount of water in the tank after 40 minutes is  

       $T = m_i + A_h + A_c - L$

substituting values  

       $T = 2000 + 1920 + 2880 - 6000$

       $T = 800 \ lb$