Topic: Fluid Mechanics
The velocity field of a certain two dimensional flow is given by V(x,y) = k(x i - y j) where k = 2/s and x and y are in meters. If the fluid density is 100 kg/m³ and pressure at origin is 10 kPa, what is the pressure at point (3,3)?
- A. 3.2 kPa
- B. 6.4 kPa
- C. 1.6 kPa
- D. None
Answer: B. 6.4 kPa
Explanation: The flow is steady and irrotational. By Bernoulli's equation, P1/rho + V1^2/2 = P2/rho + V2^2/2. At the origin (0,0), V1 = 0 and P1 = 10,000 Pa. At (3,3), velocity magnitude V2 = $\sqrt{(2*3}$^2 + (-2*3)^2) = $\sqrt{36 + 36}$ = $\sqrt{72}$ m/s. P2 / 100 + 72/2 = 10000 / 100. P2/100 + 36 = 100. P2 = 6400 Pa = 6.4 kPa.