By H. R. Vallentine (auth.)
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The minimum pressure occurs where 1- 4sin 2 8 has its minimum value, that is, where 8 = 90° and 270°, and, at these points, it follows from Eq. pU 2 - - 3. In Fig. 28 are shown the distributions of pressure along the boundary and the centre-line of a two-dimensional contraction in a horizontal plane. Of interest are the locations of points of maximum pressure, at the stagnation point S, and of minimum pressure, at X on the curved boundary outside the region of uniform low pressure 43 FLOW OF AN IDEAL FLUID and high velocity.
The three terms are known as the velocity head, the pressure head and the elevation head, respectively, and their sum, H or H' is the total head. It is evident that, in steady non-viscous flow, the total head, H', is constant along a streamline and that if, in addition, the flow is irrotational, the total head, H, is constant throughout the flow. 14 Velocity and pressure distributions Distributions of velocity can be represented either by means of a series of individual arrows, the length of each representing the velocity at its rear tip, or by means of velocity distribution curves.
The pattern of steady How of an infinite fluid in the x-direction past a cylinder of radius a at the origin, the fluid velocity at infinity being U. 52 PROBLEMS (a) Determine the velocity distributions in non-dimensional form along the x- andy-axes and on the cylinder boundary. (b) At what distances in terms of the cylinder radius from the origin along the x- andy-axes are the velocities within 1 per cent of the undisturbed velocity, U? (c) Show these non-dimensional distributions on a scale-drawing of the cylinder and axes.