Q4. (a) A metal with a cubical shape, 3.0 m x 3.0 m x 3.0 m in size, is found to have a density of 900 kg/m³. It is lowered into two layers of fluids with different densities as shown in the below Figure 4(a). Given that the densities of oil and water are 800 and 1000 kg/m³ respectively. It is found that the metal cube is just immersed under the oil surface. Find the thickness of the oil layer. 2 Qil Water 5 m 3.0 m Figure 4(a) (b) A solid cube of 1.5 m in size is immersed into the river as shown in Figure 4(b). The density of the water in the river is 1000 kg/m³. If the cube is exposed 750 mm in height over the water surface, find the density of the cube. 1.5 m 3.0 m River 750 mm Figure 4(b) (c) A rectangular gate of 20 m width is designed to separate water and another fluid as shown in Figure 4(c). Given that the densities of water and the fluid are 1000 kg/m³ and 800 kg/m³ respectively. The heights of water and the fluid retained by the gate are 5 m and 8 m respectively, calculate the resultant horizontal force acting on the gate. Gate fluid +-- F 8 m water Hinge
Q4. (a) A metal with a cubical shape, 3.0 m x 3.0 m x 3.0 m in size, is found to have a density of 900 kg/m³. It is lowered into two layers of fluids with different densities as shown in the below Figure 4(a). Given that the densities of oil and water are 800 and 1000 kg/m³ respectively. It is found that the metal cube is just immersed under the oil surface. Find the thickness of the oil layer. 2 Qil Water 5 m 3.0 m Figure 4(a) (b) A solid cube of 1.5 m in size is immersed into the river as shown in Figure 4(b). The density of the water in the river is 1000 kg/m³. If the cube is exposed 750 mm in height over the water surface, find the density of the cube. 1.5 m 3.0 m River 750 mm Figure 4(b) (c) A rectangular gate of 20 m width is designed to separate water and another fluid as shown in Figure 4(c). Given that the densities of water and the fluid are 1000 kg/m³ and 800 kg/m³ respectively. The heights of water and the fluid retained by the gate are 5 m and 8 m respectively, calculate the resultant horizontal force acting on the gate. Gate fluid +-- F 8 m water Hinge
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Transcribed Image Text:Q4. (a) A metal with a cubical shape, 3.0 m x 3.0 m x 3.0 m in size, is found to have a
density of 900 kg/m³. It is lowered into two layers of fluids with different
densities as shown in the below Figure 4(a). Given that the densities of oil and
water are 800 and 1000 kg/m³ respectively. It is found that the metal cube is
just immersed under the oil surface. Find the thickness of the oil layer.
Qil..
Water
5 m
3.0 m
Figure 4(a)
(b) A solid cube of 1.5 m in size is immersed into the river as shown in Figure
4(b). The density of the water in the river is 1000 kg/m³. If the cube is exposed
750 mm in height over the water surface, find the density of the cube.
1.5 m
3.0 m
750 mm
River
Figure 4(b)
(c) A rectangular gate of 20 m width is designed to separate water and another
fluid as shown in Figure 4(c). Given that the densities of water and the fluid
are 1000 kg/m³ and 800 kg/m³ respectively. The heights of water and the fluid
retained by the gate are 5 m and 8 m respectively, calculate the resultant
horizontal force acting on the gate.
Gate
|-|-|
fluid
water
Hinge
Figure 4(c)
8 m
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