### 1. Introduction

### 2. Hydrostatic Test

### 2.1 Definition and Procedure

### 2.2. Analysis of the Cause of Deformation and Establishment of Analysis Scenarios

### 3. Possibility of Damage to Tank Considering Water Filling Situation

*Q*= volume flow rate of member

_{i}*i*,

*A*= cross-sectional area of member

_{i}*i*, and

*V*= fluid velocity passing through member

_{i}*i*.

*Q*, of member

_{i}*i*per unit time is equal to the flow rate,

*Q*, of member

_{j}*j*per unit time, the flow rate passing through the inlet pipe of the tank is equal to the flow rate passing through the air pipe. From this, the relationship for the fluid velocities of the inlet pipe (1) and air pipe (2) can be derived as follows:

*V*

_{2}=6.25

*V*

_{1}. If we assume that it took time

*T*for filling freshwater to a specific point of the tank after opening the inlet pipe 100%, the flow rate

*Q*can be determined by multiplying Eq. (1) by the time

*T*. From this, the fluid velocity

*V*

_{1}of the water inlet part can be expressed as Eq. (3):

*P*/

*ρ*is the flow energy,

*V*

^{2}/2 is the kinetic energy, and

*gz*is the potential energy.

*z*, and Eq. (4) can be simplified to Eq. (5).

_{i}= z_{j}*V*

_{1}only. As a result,

*P*

_{1}−

*P*

_{2}, which means differential pressure, can be calculated.

^{3}, the change in fluid velocity according to the degree of opening of the inlet pipe and the pressure difference between the two pipes can be calculated using the above process, and the results for this are presented in Table 4. If a hydrostatic test is performed assuming that the diameter difference between the inlet pipe and air pipe is 2.5 times, as in the above example, there is a possibility of structural deformation caused by the pressure difference resulting from the diameter difference between the inlet pipe and air pipe.

### 4. Deformation Analysis of Tank Outer Wall

### 4.1 Modeling and Boundary Conditions

*T*,

_{x}*T*,

_{y}*T*) and rotation (

_{z}*R*,

_{x}*R*,

_{y}*R*) directions for the supports, as shown in Fig. 2.

_{z}### 4.2 Loading Conditions

^{3}. Regarding the hydrostatic pressure acting on the tank, in the 50% water filling scenario based on the tank height, a free water surface height of 4,500 mm was used, and in the 90% water filling scenario, a free water surface height of 8,100 mm was used. For example, in case 6, where the water level is 8,100 mm, pressures of 0 to 0.0794 MPa were applied to the inside of the tank filled with water for each tank height. The hydrostatic pressure was calculated by the gauge pressure, excluding the atmospheric pressure, and the gauge pressure is determined by Eq. (6): where

*ρ*is the density of the fluid,

*g*is the gravitational acceleration, and

*h*is the height to the free water surface.

### 4.3 FEA Results and Discussion

*σ*is the equivalent stress,

_{e}*β*is the element division density coefficient,

*σ*is the yield stress, and

_{Y}*K*is the material coefficient.

### 5. Theoretical Estimation of Deformation of the Tank Outer Wall

*ν*(

*x*) is the displacement from a random dot on the axis of the beam (x coordinate) in the y-direction. Beam theory and plate theory are commonly used to calculate deflection through integration of the bending moment equation (Ko and Jang, 2017). When performing calculations, the integral constant is expressed using boundary conditions, continuous conditions, and symmetric conditions. The boundary conditions refer to conditions regarding the deflection and slope at support points of the beam or plate.

*E*is the elastic modulus of the beam material,

*I*is the second moment of area for the beam section,

*M*is the bending moment,

*V*is the shear force, and

*q*is the distributed load.

*ν*′ of the deflection curve is obtained if it is integrated once, and the deflection

*ν*is obtained if it is integrated twice. The deflection is 0 at the simply supported point, and both the deflection and the inclination become 0 at the fixed end support point. As a result, the deflection in the simply supported condition indicates the largest deflection compared with other boundary conditions. The equation for beam deflection in the simply supported condition at both ends is as follows: where

*L*is the length of the beam.

### 6. Summary and Conclusion

The focus was placed on the problem of occasional deformations during the process of hydrostatic testing after installation of a tank. It was assumed that such deformation is caused by overpressure resulting from the air inside the tank, which may occur during a hydrostatic test.

It was inferred that the causes of overpressure during a hydrostatic test were low air pipe performance, diameter difference between the inlet pipe and air pipe, and fast water filling rate above the appropriate level.

To confirm that deformation occurs because of the overpressure of the internal air during hydrostatic testing of the tank, the difference in diameter between the inlet pipe and the air pipe was considered using the Bernoulli equilibrium equation in terms of flow rate. Using this example, the possibility of a pressure rise was mathematically verified.

Six deformation analysis scenarios were established using the water filling level and the air pipe performance as the variables, and FEA was conducted for the urea water storage tank. The analysis showed a large deformation of up to 37 mm.

As a result of FEA, the stress results exceeded the allowable stress of the material in the deformation analysis scenarios of cases 3, 5, and 6. In these cases, a fracture of the structure can occur. In case 3, the deflection limit was not exceeded in terms of deformation. However, it was confirmed that permanent deformation can occur as a result of plasticity in terms of the yield strength of the material.

The maximum deflection that can occur was calculated using beam theory. It was demonstrated that overpressure may actually be a cause of deformation by verifying that the approximation of the deformation obtained through FEA is included in the resulting solutions of the maximum deflection calculation.