4. (Problem 2.7) A parallel-plate flow chamber is being designed to study the adhesion of leukocytes to endothelium. The channel width is 2 cm. Determine channel heights that can be used to generate wall shear stresses (i.e., Tyx(y = -h/2) = tw) as high as 20 dyn cm² with flow rates less than 2 cm³ s¹. The viscosity of the tissue culture liquid medium is 0.0087g cm³¹ s¹.

1. A capillary tube is being used to measure the viscosity of a Newtonian liquid. The tube has a 4-cm diameter and a length of 20 cm. Estimate the viscosity coefficient for the liquid if a pressure of 2.5 kPa is required to maintain a flow rate of 1 kg/s. The liquid density is 998 kg/m3 2. Calculate the viscosity of a fluid that would allow a pressure drop of 35 kPa over a 5 – m length of 3.4 in. stainless steel sanitary pipe if the fluid is flowing at 0.12 m3/hr and has a density of 1010 kg/m3. Assume laminar flow. 3. At 2 cm diameter, 5 cm long capillary-tube viscometer is being used to measure viscosity of 10 – Pa.s liquid food. Determine the pressure required for measurement when a flow rate of 1 kg/min is desired and ρ= 1000 kg/m3.

Consider flow of blood in the microvessels of the body, assuming Poiseuille’s law holds and that the viscosity of the blood is constant. Consider a parent vessel that bifurcates into two daughter segments, all within the microcirculation and with blood flow described using Poiseuille’s law (assume that each segment has a different diameter and length).Denoting the pressure at node i by pi (i=1,2,3,4), and the flux in segment j by Qj (j=1,2,3), write down expressions for the segment fluxes in the network, in terms of the nodal pressures. How are the three volume fluxes related, and why? Assuming that the pressures at nodes 1, 3, 4 (the boundary nodes) are known, write down an expression for the pressure at the interior node, p2.

8. A large artery in a person's body can be approximated by a tube of diameter 9 mm and length 0.35 m. Also assume that blood has a viscosity of approximately 4 x 10-3 N s/m2, a specific grav- ity of 1.0, and that the pressure at the beginning of the artery is equiv- alent to 120 mm Hg. If the flow were steady (it is not) with V = 0.2 m/s, determine the pressure at the end of the artery if it is ori- ented (a) vertically up (flow up) or (b) horizontal.

Problem 3: IV Bag A 3 cm long needle at the bottom of a tube connected to an IV bag is used to inject a 125 mL of saline solution located h = 70 cm above the needle over a one hour period. The viscosity of the saline solution is 1.1 mPa.s and its density is 970 kg/m³. You may assume the resistance to flow and fluid speed in the bag and the tube is negligible - only the resistance across the needle needs to be taken into account. A. If the vein's gauge pressure is 5 mmHg, what will be the difference in the input and output pressures across the needle in both mmHg and Pa? B. What is the flow rate of the fluid, in S.I. unis? C. What is the radius of this needle in mm?

If the hematocrit of John's blood wereto change from 42% to 55% and at the same time the diameter of one ofJohn's vessels were to decrease by 1%. Using Poisselle's equation, by how much(and in what direction) would John's blood pressure have to change inorder to maintain the same volume flow rate?

K = 1.4*10-4

Determine the pressure drop over a reducer with the following conditions: Fluid density: 25 kg/m3Fluid velocity: 1.5 m/sFluid viscosity: 0.001 Pa*sInlet diameter: 0.12 mOutlet diameter: 0.019 mPipe absolute roughness: 4e-4 m Give your final answer in Pa, rounded to the nearest whole number. [Ignore entrance/exit losses and velocity loss terms]

Reynolds number for pipe flow may be expressed as Re = (4 m/ Trd) / µ Where m = mass flow, kg/s d= pipe diameter, m p = viscosity, k/m s In a certain system, the flow rate is 5.448 kg/min +0.5 %, through a 0.5" (inch) diameter (±0.005"). The viscosity is 1.92x 10-5 kg/m s, ±1 %. Calculate the value of the Reynolds Number and its uncertainty. Determine the main contribution to uncertainity.

(Permeability). A cylindrical core sample of 1 cm length and 1 cm2 cross-section has upstream and downstream pressures of 2 atm and 1 atm, respectively, during steady state flow of water at 0.997 g/s at room temperature. Calculate the permeability of the core.                                                                                Note: Water @ 25°C, viscosity = 1 cp, density of water = 0.997 g/cm3. SHOW SOLUTIONS PLS ASAP