Question 1.5.2: The U-tube shown in the figure is moved horizontally with an......

Fluid Mechanics and Hydraulic Machines [1089668]

The U-tube shown in the figure is moved horizontally with an acceleration of g/3 m/s². Find the difference of water level in its two limbs.

1.5.2

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

Slope of the free surface in the U-tube is tan θ = (g/3)/g = 1/3. Also from the figure, the slope is 2y/0.9, where y is the displacement of the liquid in the limb due to acceleration. Equating the two, we get, y = 0.15 m. Therefore, difference of water level in the two limbs is 2 × y = 0.3 m.

Related Answered Questions

Question: 1.5.5

A vertical cylindrical tank 0.5 m diameter and 1.5 m high is closed at the top. It contains water to a depth of 1.2 m, the air above the water surface is at a pressure of 39.24 kPa. Determine the pressure head on the bottom of the tank at the axis and the side, when the tank is rotated at 200 rpm ...

Verified Answer:

When the tank is rotated, the liquid free surface ...

Question: 1.5.4

A closed cylindrical vessel, 0.3 m diameter and 0.6 m high, two-third filled with oil of specific gravity 0.8 is rotated about its vertical axis. Determine the speed of rotation when (a) the oil starts touching the lid and (b) the point at the centre of the base is just clear of oil. How the ...

Verified Answer:

Given for case (a):

\mathrm{z_1 = 0.6 × 2/3...

Question: 1.5.3

A tank shown in Fig. E1.5.3 contains oil of specific gravity 0.8. If it is given an acceleration of 5 m/s² along a 30° inclined plane in the upward direction, determine the slope of the free surface and pressure at b. ...

Verified Answer:

Components of the acceleration along the horizonta...

Question: 1.5.1

A rectangular tank 3 m long, 2 m wide and 2 m deep contains water to a depth of 1.25 m. If it is accelerated horizontally at 3 m/s² in the direction of its length, find (a) (i) the inclination of the water surface with the horizontal, (ii) depth of water at the two ends, (iii) total force on the ...

Verified Answer:

(a) Equation 1.5.3 gives the slope of the free sur...

Question: 1.4.6

An 80 mm diameter composite cylinder consists of an 80 mm diameter 20 mm thick metallic plate having specific gravity 4.0 attached at the bottom of an 80 mm diameter wooden cylinder of specific gravity 0.8. Find the limits of the length of the wooden portion so that the composite cylinder floats in ...

Verified Answer:

The minimum height of the wooden portion is decide...

Question: 1.4.5

A ship displaces 49250 kN of seawater of density 1025 kg/m³. The second moment of area of the water line section about the axis through the centre is 120000 m^4 and the centre of buoyancy is 2 m below the centre of gravity. If the radius of gyration is 3.7m, calculate the period of oscillation. ...

Verified Answer:

The metacentric height is obtained from Eq. 1.4.5 ...

Question: 1.4.4

A cylindrical buoy 2 m in diameter and 1.5 m in height weighs 12 kN and floats in saltwater of density 1020 kg/m³. Centre of gravity of buoy is 0.65 m above O. If a load of 2 kN is placed on its top symmetrically, find the maximum height of the centre of gravity of this load above the bottom if the ...

Verified Answer:

Let

G_1 , G_2

and G be the centre o...

Question: 1.4.3

A barge in the shape of a rectangular block which is 8 m wide, 12.8 m long and 3 m deep floats in water with a draft of 1.8 m. The centre of gravity of the barge is 0.3 m above the water surface. State whether the barge is in stable equilibrium. Calculate the righting moment when the barge heels by ...

Verified Answer:

Centre of buoyancy will lie below the free surface...

Question: 1.4.2

A cylinder of 1.5 m diameter and 2 m long floats in seawater with its axis vertical. The base of the cylinder is 1.5 m below the water surface. Find the weight of the cylinder and the position of gravity if it is 0.3 m below the metacentre. Seawater weighs 10055 N/m³. ...

Verified Answer:

Weight of the cylinder = weight of the seawater di...

Question: 1.4.1

A cube of side a and relative density S (S < 1) floats in water. Determine the conditions for its stability if it is given an angular tilt. ...

Verified Answer:

Let x be the height of the cube immersed in water....