You will start by getting used to the idea of the linear mass density by relating it to concepts you are already familiar with: the mass and the (volume mass) density. First, you have a column of pure water that has a density PH20= 1 g/cc. The water column is in a cylinder. The column has cross-sectional area 31 cm2 and height 75 cm before salt is added. The linear mass density has two different definitions. One is going up in dimensionality, that is from the volume mass density p to the linear mass density A λ = PA where A is the cross-sectional area of the object. The other is going down in dimensionality, that is from the mass down to the linear mass density A = M where H is the height of the column in our case. You will use both of these below: (a) What is the linear mass density of the water column? ÅH20 = (b) What is the mass of the water? M = Let's now try this after adding salt to the water. When we do, the column's height rises to a level 78 cm, and we measure its salinity to 54.5 9Naci/k9H20 (grams of salt per kilogram of water). Assume that the solution is well-stirred at this point so that the salt is uniformly distributed.

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Suppose we know little about the strength of materials butare told that the bending stress σ in a beam is proportionalto the beam half-thickness y and also depends on thebending moment M and the beam area moment of inertiaI . We also learn that, for the particular case M = 2900in ∙ lbf, y = 1.5 in, and I = 0.4 in4 , the predicted stressis 75 MPa. Using this information and dimensional reasoningonly, find, to three significant figures, the onlypossible dimensionally homogeneous formula   σ=y f ( M , I ).

Horizontal stream with water with a cross sectional area of 0.1 ft2 and a velocity 40 ft/s has kinetic energy in ft.lbf/sec nearest to:ANswer: 11,7000 Fluid mechanics (please include units)

The spin rate of a tennis ball determines the aerodynamic forces acting on it. In turn, the spin rate is a§ectedby the aerodynamic torque. If the torque depends on áight speed V , density , viscosity , ball diameter D,angular velocity !, and the fuzz height, hf , Önd the important dimensionless variables for this case. Use V ,, and D as your scaling (repeating) variables.

*3.2 PQ1 A 100 mm diameter sphere contains an ideal gas at 20°C. Apply the grid method (p. 9) to calculate the density in units of kg/m³. a. Gas is helium. Gage pressure is 20 in H,O. b. Gas is methane. Vacuum pressure is 3 psi.

If the following equation is dimensionally homogeneous, find the dimensions of the physical quantity K indicated in the system of fundamental physical quantities: Length, Mass and Time. Ep -G Mm K where Ep is the gravitational potential energy (same units as the kinetic energy E mv²/2), M and m are the mass of the earth and the mass of the body, respectively, and G is the universal gravitation constant G~ 6,67 x 10-11 N m² kg²

MLT By dimensional analysis, obtain an expression for the drag force (F) on a partially submerged body moving with a relative velocity (u) in a fluid; the other variables being the linear dimension (L), surface roughness (e), fluid density (p), and gravitational acceleration (g).

Thermal conductivity k is a measure of the ability of a material to conduct heat. For conduction heat transfer in the x-direction through a surface normal to the x-direction, Fourier’s law of heat conduction is expressed as: Q=-kA.dT/dx   where ?̇ is the rate of heat transfer and A is the area normal to the direction of heat transfer. Determine the primary dimensions of thermal conductivity (k). Look up a value of k and verify that its SI units are consistent with your result. Write a set of primary SI units for k.

2. The apparatus shown below is designed to measure the density of an unknown fluid (p2₂). The two sides of the device are separated by a movable, frictionless partition. The partition is attached to the immobile sidewalls of the device via springs (different spring constants) on either side. Before pouring fluid into the device, both springs are unstretched. The device has a rectangular cross-section and extends a width w into the page. Derive an expression for the unknown density p2 = f(p1, h₁, h₂, k₁, k2, Ax, g), where Ar is the displacement of the partition relative to its equilibrium location before the fluids are poured into the apparatus. h₁ P1 k₁ 5 P2 ли Ax k₂ h₂