Chapter 6, Problem 6.1DOEP

2. Casson model was discussed in class in the context of blood rheology. This phenomenological model is often used to describe the shear stress vs. shear rate relationship in colloidal suspensions where particle aggregation might cause the measured viscosity to increase at low shear rates. In an experiment, data for the shear stress and the applied shear rate S were fitted to the Casson model written below (in a slightly different form compared to that given in the lecture notes): √t = √²₁+√as. (1) The best least square fit parameters to the experimental data were found to be 40 mPa for the yield stress to and 2.5 mPa s for the parameter a, which is referred to as the plastic viscosity. a. Using Eq. (1), derive an expression for the fluid viscosity u as a function of S. b. Plot the viscosity of the fluid as a function of S for 0.1s¹ ≤S≤ 10 s¹. c. Based on class discussion on fluid classification, how would you characterize this fluid?

Drop-load (I)This exercise is part of a series of problems aimed at modeling a situation by progressively refining our model to take into account more and more parameters. This progressive approach is very close to what professional scientists do! context We want to lower a suspended load in a controlled way, so that it hits the ground with a speed whose modulus is not too great. To do this, the suspended load (B) is connected by a rope passing through a pulley to another mass (A), which can move on a horizontal surface. To slow down the descent, we added a spring behind the mass (A).   Information The masses of the charges A and B are known.The mass of the rope itself is negligible (very small compared to the loads).The pulley has negligible mass and can rotate without friction.The charge ? is initially stationary and is at a known height h.The surface on which mass A is placed is horizontal.There is no friction between mass A and the surface on which it is placed.The string attached…

Search and define the following:(write each required formula - define its variables) 1. Impulse and Momentum2. Work Energy Principle3. Law of conservation of momentum

A particle rotates with constant speed in a circle. Let be the net torque on the particle and F the net force on the particle. Then: a. tau > 0 and F > 0 O b. tau > 0 and F = 0 . tau = 0 and F = 0 Od. tau = 0 and F > 0

Which of the following is/are not a branch of Fluid mechanics? •Cryptography •Hydraulics •Meteorology •Oceanography •Hydrology •Gas Dynamics

Drop-load (I)This exercise is part of a series of problems aimed at modelling a situation by progressively refining our model to consider more and more parameters. This progressive approach is very close to what professional scientists do! Context We want to lower a suspended load in a controlled way so that it hits the ground with a speed whose modulus is not too great. To do this, the suspended load (B) is connected by a rope passing through a pulley to another mass (A), which can move on a horizontal surface. Information The masses of the charges A and B are known.The pulley is a ring of mass mp and radius R that can rotate without friction.The surface on which mass A is placed is horizontal.There is no friction between mass A and the surface on which it is placed.The string attached to mass A is perfectly parallel to the surface on which the mass rests. SchematizationDraw a diagram of each object that interests us. Draw x- and y-axes for each object. Draw and name each force…

Archimedes established his principle while investigating a suspected fraud in the construction of a crown. The crown was made from an alloy of gold and silver instead of pure gold. Assume that the volume of the alloy was the combined volumes of components (the density of gold is 19.3g⁄(cm^3 ), the density of silver is 10.5g⁄(cm^3 )). If the crown had a weight of 9.81 N in air and 9.10 N in pure water, what percentage of gold (by weight) was it?

You are developing a porous membrane for use in a dialysis system. The membrane must be able to retain both protein and glucose on the inlet side and allow other, smaller molecules to flow through. You have found that the membrane is 0.25 mm thick and contains long, rectangular pores with a width of 0.1 microns. 57% of the 50 cm^2 membrane surface area is covered with pores. A test fluid (viscosity = 1.5 cP, density = 1015 kg/m^3) is passed through the membrane. You can assume that the test fluid has a composition similar to that of blood plasma. An initial test is run at physiological conditions, and you observe that the flow rate of fluid through the membrane is 500 cm^3/min. Given this data, what must the hydrodynamic pressure drop across the membrane in your test system be in pascals?

Mechanical EngineeringFluid Mechanics