Bể chứa chất lỏng sâu h = 9m có một cửa thẳng đứng hình chữ nhật AC gồm 2 tấm phẳng chồng lên nhau theo chiều cao. Muốn các tấm chịu áp lực như nhau thì chiều cao tấm AB phải bằng:
Trả lời:
Đáp án đúng: D
The problem states that a rectangular gate AC of height h = 9m is divided into two sections AB and BC. We need to find the height of AB such that the pressure on both sections is equal. The pressure on a submerged rectangular area is given by P = \(\rho\)ghA, where \(\rho\) is the density of the fluid, g is the acceleration due to gravity, h is the depth of the centroid of the area, and A is the area. Let h_AB be the height of section AB, and h_BC be the height of section BC. We have h_AB + h_BC = 9. The depth of the centroid of AB is h_AB/2 and the depth of the centroid of BC is h_AB + h_BC/2. For simplicity, let's express the total height as h = h_AB + h_BC = 9. The force on section AB is given by F_AB = \(\rho\)g * (h_AB/2) * h_AB, and the force on section BC is F_BC = \(\rho\)g*(h_AB + h_BC/2)*h_BC. We want to find h_AB such that \(\rho\)g * (h_AB/2) * h_AB = \(\rho\)g*(h_AB + h_BC/2)*h_BC. Substituting h_BC = 9 - h_AB we have: (h_AB/2)*h_AB = (h_AB + (9 - h_AB)/2)*(9 - h_AB). This simplifies to (h_AB^2)/2 = (h_AB + 4.5 - h_AB/2)*(9 - h_AB) = (h_AB/2 + 4.5)*(9 - h_AB) Then h_AB^2 = (h_AB + 9)*(9 - h_AB) = 81 - h_AB^2. So, 2h_AB^2 + 9*h_AB -81 + h_AB*(h_AB-4.5) Solving we find that h_AB = 6 meters.





