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

The total amount is
`T = 800 \ lb`

Step-by-step 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`