Ihave a water bath that is 3'h x 3'w x 10'l. with water flowing through the water bath (lengthwise) i need to change the water temperature from 10˚c to 40˚c and then back to 10˚c again in 3 complete cycles. so 10-40-10-40-10-30 (it ends at 30˚c).

ideally the process can be completed in 10 min there are 3 water tanks, one at 80˚c, one at 10˚c, and one buffer tank to be used to recycle as much of the warmest water as possible. the buffer tank and the hot water tank will alternate after each use as the recycled water will be heated back up to 80˚c. the water blends the hot and cold water tanks to supply the water temperatures required between 11˚c and 40˚c.

i have 3 questions:

1) what volume do i require the hot and cold water tanks to hold?
2) what flow rate would be required to achieve these temperature changes over a 10 min interval?
3) how much water will not be able to be recycled in each full cycle?

Answer8.0m;

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

//(b) both involve the use of levers;