Question 1 of 4 · Flow Kinematics and Continuity · Advanced · About 24 min

Inspect a two-dimensional ventilation field

A measured, steady, two-dimensional air velocity field in a test region is $u(x,y)=2.0+0.50x$ and $v(x,y)=1.50-0.50y$ , with velocities in when are in metres. At the point , determine the local velocity components, speed, direction counterclockwise from the positive axis, and the two Cartesian components of material acceleration. Neglect any out-of-plane motion.

Point P in a two-dimensional velocity field with coordinate projections and direction arrows. — Schematic, not to scale unless dimensions are given.

Given

u(x,y)=2.0+0.50x m/s
v(x,y)=1.50−0.50y m/s
Point P: x=2.0 m, y=1.0 m
Steady flow

Find

u and v at P
Speed at P
Velocity angle
a_x and a_y at P

Assumptions

Velocity field differentiable over the region.
Coordinates in metres.

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Inspect a two-dimensional ventilation field

Given

Find

Assumptions

Worked solution