The velocity in a certain two-dimensional flow field is given by the equation NS

generals336

generals336

Answered question

2021-09-17

The velocity in a certain two-dimensional flow field is given by the equation
V=2xti^2ytj^
where the velocity is in ft/s when x, y, and t are in feet and seconds, respectively. Determine expressions for the local and convective components of acceleration in the x and y directions. What is the magnitude and direction of the velocity and the acceleration at the point x = y = 2 ft at the time t = 0?

Answer & Explanation

tabuordg

tabuordg

Skilled2021-09-18Added 99 answers

Consequently, the notation in terms of rectangular coordinates means that a fluid particle's velocity depends on where it is situated within the flow field (as indicated by its coordinates, x, y, and z) and when it occupies the specific point (as determined by the time, t). The use of three rectangular components to represent the velocity is also convenient. According to the task's data, the 
V=2xti^2ytj^ 
alocal=d dt (2xti^2ytj^) 
alocal=2xi^2yj^ 
alocal=2xi^2yj^ 
At a given point x=y=2, we have 
alocal=4i^4j^ 
|a|=42+42 
Now we will determine conective acceleration 
aconv=UdU dx +VdV dx  
U=2xt 
V=2yt 
aconv=2xtd dx (2rti^2ytj^)2ytd dy (2xti^2ytj^) 
aconv=4t2xi^4t2yi^

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