Question

Adverse pressure gradient implies that ______.

• A. pressure decreases in the direction of flow
• B. pressure increases in the direction of flow
• C. pressure is zero everywhere within the flow field
• D. pressure is uniform (non-zero) everywhere within the flow field

Hint:

Think about whether the pressure change is pushing the flow forward or holding it back near a wall.

Answer 1

The Correct Option is B

Step 1: Write the boundary layer momentum balance near a wall.
Close to a solid wall the fluid velocity is nearly zero, so the momentum equation there reduces mainly to a balance between the pressure gradient and the wall shear stress, roughly $\mu \left(\dfrac{\partial^2 u}{\partial y^2}\right)_{wall} = \dfrac{dp}{dx}$.

Step 2: Read what a positive $dp/dx$ does to the flow.
If $dp/dx$ is positive, pressure is rising along the flow direction $x$. That pressure rise acts like a brake on the slow moving fluid inside the boundary layer, decelerating it further and, if strong enough, pushing it backward and causing separation.

Step 3: Name this condition.
A positive $dp/dx$, meaning pressure increasing along the flow direction, is defined as an adverse pressure gradient because it opposes the flow instead of assisting it.

Final Answer:
So the defining condition is pressure rising in the direction of flow. \[ \dfrac{dp}{dx} > 0 \implies \text{adverse pressure gradient} \]