The x component of velocity in an incompressible flow field is given by u = Ax, where A = 2 s-1 and the coordinates are measured
in meters. The pressure at point (x, y) = (0, 0) is p0 = 190 kPa (gage). The density is rho = 1.50 kg/m3 and the z axis is vertical. (a) Evaluate the simplest possible y component of velocity. (b) Calculate the fluid acceleration and (c) determine the pressure gradient at point (x, y) = (2, 1). (d) Find the pressure distribution along the positive x axis.
1 answer:
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Answer:
6.37 inch
Explanation:
Thinking process:
We need to know the flow rate of the fluid through the cross sectional pipe. Let this rate be denoted by Q.
To determine the pressure drop in the pipe:
Using the Bernoulli equation for mass conservation:
thus
The largest pressure drop (P1-P2) will occur with the largest f, which occurs with the smallest Reynolds number, Re or the largest V.
Since the viscosity of the water increases with temperature decrease, we consider coldest case at T = 50⁰F
from the tables
Re= 2.01 × 10⁵
Hence, f = 0.018
Therefore, pressure drop, (P1-P2)/p = 2.70 ft
This occurs at ae presure change of 1.17 psi
Correlating with the chart, we find that the diameter will be D= 0.513
= <u>6.37 in Ans</u>