If the pressure at point A 2 m 2 m is 175 kPa what is the pr

If the pressure at point A (2 m, 2 m) is 175 kPa, what is the pressure at B (4 m, 2 m)? Recall the velocity field is V = {(3x)i - (3y - 1)j}m/s. Take p = 1600kg/m^3. Express your answer in kPa to three significant figures. P_B =

Solution

Total pressure remains constant.

Total Pressure = Static pressure + Dynamic pressure

P_t = P_s + 1/2* rho*V²

P_sa + 1/2* rho*V_a² = P_sb + 1/2* rho*V_b²..............eqn1

We have V = 3xi - (3y-1)j

Velocity at A(2,2) V_a = 3*2i - (3*2-1)j

= 6i - 5j

|V_a| = sqrt(6² + 5²) = sqrt61 m/s

Velocity at B(4,2) V_b = 3*4i - (3*2-1)j

= 12i - 5j

|Vb| = sqrt(12² + 5²) = 13 m/s

Putting these values in equation 1 we get,

175*10³ + 1/2*1600*(sqrt61)² = P_b + 1/2*1600*13²

P_b = 88600 Pa = 88.600 kPa