Question 3: As will be discussed in future lectures, the volume rate of flow, Q, through a pipe can be determined by means of a flow nozzle located in the pipe as illustrated in the figure below. The nozzle creates a pressure drop, pA - pB, along the pipe which is related to the flow through the equation Q = K∑(pA - pB), where K is a constant depending on the pipe and nozzle size. The pressure drop is frequently measured with a differential U-tube manometer of the type illustrated in the figure. If the specific weight of a fluid is defined as: ̳ = ̱g, where ̱ is the fluid density and g is the acceleration due to gravity:
a) Determine an equation for pA - pB in terms of the specific weight of the flowing fluid, ̳1, the specific weight of the gage fluid, ̳2, and the various heights indicated.
b) For ̳1 = 9.80 kN/m^3, ̳2 = 15.6 kN/m^3, and h2 = 0.5 m, what is the value of the pressure drop, pA - pB?