Question

na obnerence yorm Flease sShow work & state assumptions. In the human lymphatic system, the spleen works to filter out old or damaged red blood cells and to create white blood cells (leukocytes). The spleen allows healthy red blood cells (erythrocytes) to pass through and uses lymphocytes, a type of white blood cell, to break down unhealthy erythrocytes into components that can be saved and reused to make new red blood cells. The average human body contains 4.968355 L of blood (p 1.060 g/cm3, H- 3.5 x 103 Pa*s) with blood composition (in volume percent) of 55% plasma, 40% erythrocytes, 1 % leukocytes and approximately 2.6% platelets (thrombocytes). Lymph fluid has a composition similar to blood plasma and contains white blood cells. Blood travels through the ascending aorta of the human heart (with an average diameter of 1.1417 inch or 29 mm) at an average speed of 3.5 miles/hr (1.56464 mt/s). The specific gravities of human blood, all blood cells and red blood cells are l .060, 1.0971, and 1.103 respectively. Tonsils Thymus Gland ymph Nodes Bone MarrTOW LYMPHATIC SYSTEM 1. A patient has been diagnosed with slight symptoms of lymphedema of the accumulation of fluid in the lymphatic system typically caused by cancer or enlarged lymph nodes. Patient measurements were taken of the lymphatic network of the lower leg with an average lymphatic pressure of 8.5 mm Hg (or 1133.24 Pa), an initial diameter of the lower leg lymphatic vessel network of 54.8 m (or 2.1575 x 10° inch) and a lymphatic vessel range of 9.25 mm (or 0.3642 inch) If the average initial velocity of the lymph fluid is measured using dye measurements to be 2.75 mm/s (or 0.1083 inch/s) with a lymphatic vessel area expansion factor of 3.45, estimate the lymphatic fluid exit velocity in meters per second from the vessel network using the Mechanical Energy Equation and explain your answer (55 POINTS) -3 2.Find the friction factor for the blood flow provided in the aorta for abovementioned information. If this person is chased up a steep mountain hill by Michael Myers on Halloween night and their blood velocity increases to 6.38 m/s assuming no heart failure or any other premature negative result, please determine the new friction factor using th Moody Chart and the Colebrook Equation (please show all work). Determine the percent error between these values and briefly explain your results (45 POINTS)

Answer 1

Normal and tumor tissues have properties like those of the porous medium. Darcy's empirical observations show that the fluid velocity in porous media is proportional to the pressure gradient,

The lymphatic vessel can be represented as a pipe with changing a radius 'R' and assuming that lymph is an incompressible Newtonian fluid

Therefore fluid transport in the porous media can be described by the following equation:

V_i = -KVp_i,

Where,

P_i is the interstitial pressure

K is the hydraulic conductivity of the interstitium

V_i is the interstitial fluid velocity

The mass balance equation for a steady state incompressible fluid shows that the divergence of velocity is zero. (or)

mathematically

This equation is acceptable for porous media when there is no fluid source. For instance, between the interstitial space and blood or lymph vessels, fluid is exchanged, therefore, the steady-state incompressible form of the continuity equation must be modified

2. The flow rate in each vessel is calculated by applying mass (or volumetric flow rate) conservation law at each junction of the network. The equation representing the volumetric flow rate for an interconnecting point is :

The friction factor can be equated by :

Where:

'f' is the Friction factor and dimensionless

'D' is the inside diameter