First slide

Fluid statics

Question

A car containing a beaker of water is moving horizontally on a level road. Consider two points, A & B, inside the water such that they are on the same horizontal level and are separated by a distance L. Which of the following options is correct regarding the pressure differences between those two points?

Easy

A

If car is accelerating with acceleration a, P_A – P_B = ρgL
B

If car is accelerating with acceleration a, P_A – P_B = 0
C

If car is moving with constant velocity, P_A – P_B = 0
D

If car is moving with constant acceleration a, P_A – P_B = ρ (g+a)L

Solution

When the car is moving with constant velocity, points on the same horizontal level will have the same pressure.
So, P_A – P_B = 0.
When the car moves with constant acceleration the pressure difference between those two points will be ρaL,
as the pressure difference will be responsible for providing acceleration to the small fluid column of volume (L.dA) between points A & B
(where dA is an area of small element that we think of).

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