18.4. Examples and Applications

Try these first

1. 1.

   What does the conservation of momentum state?

   Hint

   Consider forces acting on the system.

2. 2.

   What is hydraulic conductivity?

   Hint

   Think about how water moves through soil.

3. 3.

   What principle states that momentum is conserved in a fluid system?

   • Bernoulli's Principle
   • Law of Conservation of Momentum
   • Pascal's Principle

   Hint

   Think about the implications of momentum in a flowing fluid.

4. 4.

   True or False: The Reynolds Transport Theorem is used to evaluate fluid properties in a control volume.

   • True
   • False

   Hint

   Recall how we analyze flows within defined volumes.

5. 5.

   A cylindrical tank has an inlet delivering water at varying rates. If the inflow is given by Q(t) = 0.1 + 0.05t (in L/s), and the outlet is set to a constant Q_out of 0.15 L/s, determine the volume of water in the tank after 10 seconds.

   Hint

   Use integral calculus for inflow and consider permanence of outflow.

6. 6.

   Two streams of water flow into a T-joint, with flow rates Q1 = 5 m³/hr from one pipe and Q2 = 3 m³/hr from another. If the design for the output flow must not exceed 7 m³/hr, determine the max output flow rate that ensures momentum conservation is maintained.

   Hint

   Apply conservation principles while analyzing the combined output.