Q u AKAA

b What is the volume per second flowing past cross-section 2 in Figure 2.8(a)?

Figure 2.8 For Problem 2.1. Venturi meters for measuring flow in a pipe. (a) Smooth contraction in diameter along the pipe. (b) Sharp-edged orifice.

c The pressures p1 and p2 are measured by the heights of columns of fluid rising up the side tappings, as shown in Figure 2.8(a). Indicate on the diagram a distance corresponding to the factor in square brackets in the expression in Problem 2.1(a). d Figure 2.8(b) shows a similar system for measuring flow in a pipe of nominally uniform cross-section. A plate with a sharp-edged hole in it is inserted as shown, and the pressure is measured on either side. Will the flow rate calculated from the equation of Problem 2.1(a) be correct, too high or too low? Why?

Hint: Consider the full energy equation (2.1).

2.2 A two-dimensional nozzle discharges water, as a plane horizontal jet of thickness t and width b. The jet then strikes a large inclined flat surface as shown in Figure 2.9.

a Neglecting the effects of gravity and viscosity, apply Bernoulli's equation to show that u1 = u2 = Uj.

Hint: The pressure change across a thin layer is negligible.

b What is the component parallel to the plane of the force acting on the fluid? By considering the change in momentum of the fluid in a suitable control volume, and applying conservation of matter, show that the flow rates up and down are, respectively,

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