A rectangular block below of height L and horizontal cross-sectional area A floats at the interface between two immiscible liquids:  Derive a formula for block density(ρb), in terms of the fluid densities ρ1 and ρ2, heights h0 and h1, and the cross-sectional area A. (Note, all variables may not appear in the final result).

A pair of concentric glass cylinders, with diameters of 1 and 1.05 cm, respectively are held together in such a way that both annular ends are open to the flow of fluids. The pair of cylinders with its axis vertical are so placed that the open end is slightly below the surface of a reservoir of silicone oil at 25 deg. C. What is the expected height of the oil into the annular space between the cylinders? Take o=0.019 N/m and p=900 kg/m³.

2. Consider a flow of liquid in a horizontal circular tube which is mobile. The flow in the tube is assumed to be fully developed and pressures at two ends are Po and PL. The cylindrical tube has radius of R and length of L. The tube itself is moving along the z-direction with a velocity of Vz (R) = -α Trz (R), where a > 0. a) Obtain the radial velocity profile in the circular tube. b) Find the average velocity Hint (Answer): R Z Fluid flows in z- direction L Uz = ΔΡ 4μL ΔΡ 2L - R21 2μ ΔΡ Uavg=8μL R²+ ΔΡ 2L aR - R2V 2μ

An enclosure consists of two black surfaces formed by cutting off a 0.3 m diameter spherical shell by a plane at a distance 0.1 m from the centre and closing it by a black circular disk Determine the view factors of the surfaces. in R de

Problem 3: A model equation for chemical reactive flow in a one-dimensional reactor is given as ac ac +u. ôt dx :DOC-KC, where C is the dimensionless concentration of the species, u is the velocity, D is a diffusion coefficient, k is a reaction rate, and x,t are the distance from the reactor and time, respectively. (3a) Determine the dimensions of D, k;

The pressure drop in a 6-in. pipe (I.D. = 6.065 in.) of length L is 1 psi with the flow in the highly turbulent region. If the same liquid flows at the same volumetric flow rate in a 3-in. pipe (I.D. = 3.068 in.) with length L, the pressure drop (psi) is:

Suppose that exactly half of the annular volume between concentric, horizontal cylinders is filled with a liquid and half with a gas, as shown below on the left. When the inner cylinder is rotated at an angular velocity , it is found that one interface rises to a height H above the other. The gap between the cylinders is sufficiently thin (W<< R) that local Cartesian coordinates can be used, as shown on the right. (For clarity, the gap width is exaggerated on the left.) All of the following questions concern flow in the liquid, which is Newtonian with constant properties. g R+W Gas Ω Liquid R H y Enlargement of liquid-filled gap X W ΩR Fixed (a) Assuming steady, fully developed flow, determine Vx(y) in the liquid in terms of dp/dx. (At this point, dp/dx is unknown.) (b) Relate dIP/dx in the liquid to H. You can assume that the absolute pressure in the gas is nearly constant (P = Po) and that surface tension is negligible. (c) Calculate H. That is, relate H to the rotation rate (),…

2.8. *The deepest point in the oceans of the world is believed to be in the Marianas Trench, southeast of Japan; there the depth is about 11 000 m. What is the pressure at that point?

plz answer both 2 questions

HOMEWORK-2 Considering the steady-state laminar flow of a liquid with density p and viscosity p in a vertical tube of length L and radius R; a) Show the momentum flux and velocity profile in the figure. b) Determine the momentum flux distribution, the velocity distribution, the maximum velocity (Vzmax), and the average velocity (Vzaverage) expressions. PL L R ! Po 1111111 Flow in