Answer to Question #3240 in Mechanics | Relativity for Baffa Tijjani

Question

Please. How can I derive the units of this quantities

1.
a. Viscosity

b. The specific heat capacity

c, Density

d. Pressure

2. 10km to SI unit, 5 hrs, 100g, 65cm, 96mm.
3. 100g/cm3 to kg/m3, 0.2km/h to m/s, 5m/s to cm/s, 580mm/h to m/s.

Answer 1

1a. Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress. In everyday terms (and for fluids only), viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement (fluidity).
Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction. For example, high-viscosity felsic magma will create a tall, steep stratovolcano, because it cannot flow far before it cools, while low-viscosity mafic lava will create a wide, shallow-sloped shield volcano. All real fluids (except superfluids) have some resistance to stress and therefore are viscous, but a fluid which has no resistance to shear stress is known as an ideal fluid or inviscid fluid.
The applied force is proportional to the area and velocity gradient in the fluid. Combining these three relations results in the equation:
F=Aμu
where μ is the proportionality factor called viscosity.

So for units we have
[Newtons]=[metres² ][1/second][μ]→[μ]=[Pascals*sec].

b. c=Q/∆T=Joules/Kelvin.

c. ρ=M/V=kilograms/metres³

d. P=F/s=Newtons/metres²

2. 10 km = 10*1000 meters=10000 meters; 5hrs=5*3600 sec=18000sec; 100 g = 0.1 kg; 65 cm=0.65 m;
96 mm = 96*0.001 m=0.096m.

3. 100 g/ cm³ = 100*0.1/0.01*0.01*0.01kg/m³ = 10000 kg/m³;
0.2 km/h=0.2*1000/3600 m/s = 0.05m/s;
5m/s = 50cm/s;
580mm/h = 580*0.001/3600 m/s = 1.6*10^-4m/s.