1.3 KiB
Homework 5 - Aidan Sharpe
1
If the specific weight, \gamma, of a substance is 8.2[kN/m$^3$], what is its mass density, \rho, in kg/m$^3$?
On Earth, 9810[kg] weighs 1[kN], so an object that weighs 8.2[kN] will have a mass of 80442[kg]. Therefore, $\rho = 80442$[kg/m$^3$].
2
A fluid flowing between two parallel plates has a viscosity, $\mu = 0.62$[Ns/m$^2$], and density, $\rho = 1250$[kg/m^3]. Calculate the intensity of shear stress, \tau, in pascals at $y = 3$[cm], assuming a straight-line viscosity distribution, given that the top plate has a velocity of 100[cm/s] and the fluid is 6[cm] thick.
Velocity at $y = 3$[cm]:
\tau = \mu{du \over dy} = 0.62\left(0.03 \times {1 \over 0.06}\right) = 0.31\text{[Pa]}3
A cube with side length 10[cm] is placed into two different liquids. In the first liquid, the top of the cube is $h_1 = 1$[cm] above the surface. In the second liquid, the top of the cube is h_2 above the surface. If the densities of the liquids are known to be $\rho_1 = 1000$[kg/m$^3$], and $\rho_2 = 1300$[kg/m$^3$] respectively, find h_2.
Displaced mass for liquid 1, same as mass of cube:
0.1 \times 0.1 \times (0.1 - 0.01) \times 1000 = 0.9\text{[kg]}Displaced mass for liquid 2:
0.1 \times 0.1 \times (0.1 - h_2) \times 1300 = 0.9\therefore h_2 = 0.031\text{[m]} = 3.1\text{[cm]}