Case study C

Part One

In many industrial processes flow and pressure measurement is a vital and an integral part. The transportation of fluids relies on accurate measurement of their flow. In this project, the equipment that will be suitable to measure the pressure and flow rate of beer during transportation is orifice plate. It is created by inserting an obstructing place in the pipe which has a round hole at the center which measures the pressure on each side of the orifice (Oliveira et al. 2009). The plates are trapped between two pipe flanges. Pressure taps on each flange make it possible to measure the Pressure differential across the plate. The dimensions of the plate and the pressure differential are combined with particular properties of the fluid which in this case is beer to determine the flow rate of the fluid through the pipe, thus, making it the best instrument to measure pressure and flow rate of beer in this case. Bernoulli’s equation is used for the calculation of the incompressible liquid flow

∆P=1/2 ρV_2^2-ρV_2^2

Given physical layout of a pipe, the equation can be modified to fit the dimensions of the pipe rather than velocity. Also, the equation perfectly assumes laminar flow which is not true in the real world since there is some amount of turbulence in the flow that converts kinetic energy into heat thus adding discharge coefficient (Cd ).

Q=〖C_d〗_√(2(P_(1-P_2 ) )/ρ ×A2/√(1-[A2/A1]^2 ))

Part two

Fluid is a substance that has no fixed shape and continually flows under applied shear stress. However, its properties determine how fluid can be used in technology and engineering as well as its behavior in fluid mechanics. The properties of a fluid comprise of density (ρ), which increases with the increase of the pressure of a liquid and decreases with increase in temperature and the density of any liquid is found by P= ρRT, where P is pressure, R is universal gas constant, and T is temperature. Viscosity is another fluid property that determines the amount of fluid resistant to shear stress. It decreases with increase in temperature of a liquid. Temperature is another liquid property that determines the degree of coldness or hotness of or heat intensity level of a fluid. It is measured in Kelvin scale which is widely used in engineering because it’s independent of properties of a substance, Celsius scale, and Fahrenheit scale. Pressure is the fluid force per unit area, denoted as P (Elger, Donald F., and John A. Roberson, 2016). There is also the specific volume property which is a volume that a fluid occupies per unit mass, a specific weight which is weight possessed by unit volume of a fluid which differs with changes in acceleration and specific gravity which is the ratio of the specific weight of the given fluid to the specific weight of the standard fluid. Some of the application includes; making glass objects of varying shapes though glass melting and pouring into molds due to the liquid flowing nature (viscosity) and ability to take the shape of a container. Water pumps also use the properties of a fluid (ability to flow and differences in pressure).

The equation of state as applies to fluids

PV= mRT{R is Universal Gas Constant)

P=(m/V)RT

P= ρRT (since ρ=m/V)

M =Mass

V=volume

P=Pressure

T=Temperature

BIBILIOGRAPHY

Oliveira, J.L.G., Passos, J.C., Verschaeren, R. and van der Geld, C., 2009. Mass flow rate measurements in gas–liquid flows by means of a venturi or orifice plate coupled to a void fraction sensor. Experimental Thermal and Fluid Science, 33(2), pp.253-260.

Elger, D.F. and Roberson, J.A., 2016. Engineering fluid mechanics (pp. 170-185). Hoboken (NJ): Wiley.