Fluid Mechanics Multiple Choice Questions on “Pressure Distribution in a Fluid – 1”.

1. Which one of the following is the unit of pressure?

a) N

b) N/m

c) N/m^{2}

d) N/m^{3}

Answer: c

Clarification: Pressure is defined as the force per unit area acting normal to a surface. The SI unit of force is N and area is m^{2}. Thus, the unit of pressure will be N = m^{2}.

2. Which one of the following is the dimension of pressure?

a) [MLT^{2}].

b) [MLT^{-2}].

c) [ML^{-1}T^{2}].

d) [ML^{-1}T^{-2}].

Answer: d

Clarification: Pressure (p) is defined as the force (F) per unit area (A) acting normal to a surface.

Thus,

3. Which one of the following statements is true regarding pressure?

a) Pressure is a scalar quantity

b) Pressure is a vector quantity

c) Pressure is a scalar quantity only when the area is infinitesimally small

d) Pressure is a vector quantity only when the area is infinitesimally small

Answer: a

Clarification: Pressure is defined as the force per unit area acting normal to a surface. Both force and area are vectors, but the division of one by the other leads to a scalar quantity.

4. A beaker half-filled with water is exposed to the atmosphere. If the pressure at points A, B and C as shown are P_{a}, P_{b} and P_{c} respectively, which one of the following will be the relation connecting the three?

a) P_{a} > P_{b} = P_{c}

b) P_{a} > P_{b} > P_{c}

c) P_{a} < P_{b} < P_{c}

d) P_{a} < P_{b} = P_{c}

Answer: d

Clarification: Since the beaker is exposed to the atmosphere, the pressure at point A will be atmospheric, P_{a} = 0. Pressure increases in the vertically downward direction, P_{a} < P_{b} and P_{a} < P_{c}.

Pressure remains constant in the horizontal direction, P_{b} = P_{c}. Therefore, P_{a} < P_{b} = P_{c}.

5. A beaker is filled with a liquid up to a height h. If A and B are two points, one on the free surface and one at the base as shown, such that the minimum distance between the two is l, what will be the pressure at point B?

Answer: b

Clarification: For a constant density liquid, pressure varies linearly in the vertically downward direction. Thus,

P_{B} = P_{A} + ρgh

where P_{B}=Pressure at B, P_{A}=Pressure at A, ρ=density of the liquid, g=acceleration due to gravity and h=vertical distance seP_{A}rating the two points. Since A is at the free surface, P_{A} = 0, P_{B} = ρgh.

6. A beaker of height h is filled with a liquid of density ρ up to a certain limit. The beaker is rotated by an angle θ such that further increase in the angle will result in over flow of the liquid. If the liquid surface is exposed to the atmosphere, what will be the gauge pressure at point B?

a) ρgh

b) ρgh sin θ

c) ρgh cos θ

d) ρgh=2

Answer: c

Clarification: Vertical distance below the free surface at which the point B is located will be h cos θ.

Since the pressure at the free surface is atmospheric, the gauge pressure at B will be = 0 + ρgh cos θ.

7. An arm of a teapot is completely filled with tea (density=ρ) If the arm has a length of l and is inclined at 30^{o} to the horizontal, what will be the pressure difference between the two points, C at the mouth and D at the base of the arm?

a) ρgl

b) ρgl/2

c) √2ρgl

d) 2ρgl

Answer: b

Clarification: Vertical distance difference between the two points, C at the mouth and D at the base of the arm will be l sin θ = l sin 30^{o} = l=2. Thus, pressure difference between C and D is = ρgl/2.

8. A beaker is filled with a liquid of density ρ_{1} up to a certain height. The pressure at the base of the beaker id P_{b}. If the liquid is replaced by an equal volume of another liquid of density ρ_{2}, what will be the pressure at the base of the beaker now?

Answer: d

Clarification: P_{B} = ρ1gh, where h=height up to which the liquid is filled. Since equal volume of the second liquid is poured, it’ll also rise to a height of h. Thus, the pressure at the base will become