Accelerating closed tank completely filled with oil: When the tank moves with a horizontal acceleration, the pressure at the back (rear) end becomes greater than at the front end. State whether this statement is correct.

Introduction / Context:In accelerating containers, a hydrostatic-like pressure gradient develops in the direction opposite to the acceleration because the fluid experiences an apparent body force. This question checks understanding of pressure distributions in non-inertial frames for a completely filled closed tank.

Given Data / Assumptions:

• Tank is completely filled (no free surface).
• Horizontal acceleration a to the right (for example).
• Incompressible fluid and steady acceleration.
• No sloshing because there is no free surface.

Concept / Approach:In a non-inertial frame accelerating to the right, a uniform body force per unit mass acts to the left with magnitude a. The pressure gradient satisfies dp/dx = ρ * a (with x measured opposite to the apparent body force). Consequently, pressure increases linearly toward the rear end (left side) and decreases toward the front end (right side).

Step-by-Step Solution:

Verification / Alternative check:In an open tank with a free surface, the surface tilts with slope a/g. In a completely filled tank, instead of a surface tilt, the same physics appears as a linear pressure gradient. Both pictures are consistent with higher pressure at the rear for forward acceleration.

Why Other Options Are Wrong:

• Incorrect: Violates the basic non-inertial equilibrium relation.
• Only true for open tanks: Not required; closed tanks also exhibit the gradient.
• Only true if compressible: Compressibility is not required for establishing the gradient.

Common Pitfalls:Assuming pressure must be uniform because the tank is “closed”; confusing acceleration effects with elevation head alone; believing a gradient appears only when a free surface is present (it is a general inertial effect).

Final Answer:Correct