Water flowing in x direction has a rare of Bx = 3yz liters/minute/m square. The total flow or flux of water through the rectangular area with corner (0 0 0), (0 3 0), (0 0 2) and (0 3 0) m is:

 

Flux of Water Through a Rectangular Surface

The water flow is along the x-direction with flow rate density:

B_x = 3yz   liters/min/m²

The rectangular surface lies in the yz-plane at x = 0, with:

• 0 ≤ y ≤ 3
• 0 ≤ z ≤ 2

Step 1: Write the Flux Integral

Φ = ∫₀³ ∫₀² 3yz dz dy

Step 2: Integrate with Respect to z

Φ = ∫₀³ 3y [ z² / 2 ]₀² dy

= ∫₀³ 3y × 2 dy

= ∫₀³ 6y dy

Step 3: Integrate with Respect to y

Φ = 6 [ y² / 2 ]₀³

= 3 × 9

= 27

Total Flux = 27 liters/min