a masonry dam 7m high has a top width of 1.5 metres and bottom width of 5 metres.maximum water level in the dam is 1m below the top of the dam. determine the maximum and minimum pressure intensities at the base when the dam is full. take weight of water as 9.81KN/m3 and weight of masonry as 21.6KN/m3.
Well, well, well! Let's dive into the world of masonry dams, shall we? Brace yourself for some dam-tastic calculations!
To find the maximum and minimum pressure intensities at the base when the dam is full, we need to consider the weight of both the water and the masonry.
First things first, let's calculate the maximum pressure intensity at the base of the dam:
Step 1: Calculate the weight of the water above the maximum water level:
The volume of water above the maximum water level is the difference between the volume of a trapezoidal prism and the volume of a triangular prism.
Volume of trapezoidal prism = (1/2) x (1.5 + 5) x 7 x 1 (since the top width is 1.5m and the bottom width is 5m)
Volume of triangular prism = (1/2) x 1.5 x 7 x 1 (since the top width is 1.5m)
Volume of water above maximum level = Volume of trapezoidal prism - Volume of triangular prism
Now multiply the volume by the weight of water to find the weight:
Weight of water above maximum level = Volume of water above maximum level x 9.81KN/m3
Step 2: Calculate the weight of the masonry:
The volume of the masonry is the same as the volume of the trapezoidal prism.
Volume of masonry = (1/2) x (1.5 + 5) x 7 x 7 (since the height is 7m)
Now multiply the volume by the weight of masonry to find the weight:
Weight of masonry = Volume of masonry x 21.6KN/m3
Step 3: Calculate the maximum pressure intensity:
The maximum pressure intensity at the base of the dam is the sum of the weight of the water above the maximum level and the weight of the masonry, divided by the base area:
Maximum pressure intensity = (Weight of water above maximum level + Weight of masonry) / Base area
Now, let's repeat the above steps to find the minimum pressure intensity:
Step 1: Calculate the weight of the water below the maximum water level:
The volume of water below the maximum level is the volume of a rectangular prism.
Volume of water below maximum level = 1.5 x 7 x 1 (since the top width is 1.5m)
Weight of water below maximum level = Volume of water below maximum level x 9.81KN/m3
Step 2: Calculate the minimum pressure intensity:
The minimum pressure intensity at the base of the dam is the weight of the water below the maximum level, divided by the base area:
Minimum pressure intensity = Weight of water below maximum level / Base area
After following these steps, you'll have both the maximum and minimum pressure intensities at the base of the dam. Remember, safety first, so never underestimate the importance of those pressure calculations!
To determine the maximum and minimum pressure intensities at the base of the dam when it is full, we need to consider the weight of water and the weight of the masonry.
Step 1: Calculate the maximum pressure intensity at the base of the dam.
The maximum pressure intensity occurs at the base of the dam when it is full. We can calculate this using the weight of water.
Given:
Height of the dam (h) = 7 m
Top width of the dam (b1) = 1.5 m
Bottom width of the dam (b2) = 5 m
Water weight (γw) = 9.81 kN/m3
The maximum pressure intensity formula is:
Maximum Pressure Intensity = γw * (h + 0.5 * (b1 + b2))
Substituting the given values into the formula, we get:
Maximum Pressure Intensity = 9.81 * (7 + 0.5 * (1.5 + 5)) kN/m2
Calculating this, we find that the maximum pressure intensity at the base of the dam when it is full is:
Maximum Pressure Intensity = 9.81 * (7 + 0.5 * 6.5) kN/m2
Maximum Pressure Intensity = 9.81 * (7 + 3.25) kN/m2
Maximum Pressure Intensity = 9.81 * 10.25 kN/m2
Maximum Pressure Intensity = 100.2025 kN/m2
Step 2: Calculate the minimum pressure intensity at the base of the dam.
The minimum pressure intensity occurs at the base of the dam when the water level is 1 meter below the top of the dam. This means the height of the water column is 6 meters.
Given:
Water weight (γw) = 9.81 kN/m3
Height of water column (h) = 6 m
The minimum pressure intensity is the same as the maximum pressure intensity, as it is independent of the water level. Therefore, the minimum pressure intensity at the base of the dam when the water level is 1 meter below the top is also:
Minimum Pressure Intensity = 100.2025 kN/m2
Therefore, the maximum and minimum pressure intensities at the base of the dam when it is full are 100.2025 kN/m2.
To determine the maximum and minimum pressure intensities at the base of the dam when it is full, we need to consider the weight of the water and the weight of the masonry.
Let's start by calculating the maximum pressure intensity at the base when the dam is full.
1. Calculate the weight of the water:
The weight of the water can be found using its density and the volume of water. The density of water is given as 9.81 kN/m³, and the volume of water can be calculated using the dimensions of the dam.
Volume of water = (1.5 + 5) / 2 * 7 * 1
Weight of water = Volume of water * Density of water
2. Calculate the weight of the masonry:
The weight of the masonry can be found using its density and the volume of masonry. The density of masonry is given as 21.6 kN/m³, and the volume of masonry can be calculated using the dimensions of the dam.
Volume of masonry = (1.5 + 5) / 2 * 7 * 6
Weight of masonry = Volume of masonry * Density of masonry
3. Calculate the maximum pressure intensity:
The maximum pressure intensity at the base occurs when the dam is full, so we add the weight of water and the weight of masonry to get the maximum pressure intensity at the base.
Maximum pressure intensity = Weight of water + Weight of masonry
Now, let's calculate the values using the given data:
1. Calculate the weight of the water:
Volume of water = (1.5 + 5) / 2 * 7 * 1 = 24.5 m³
Weight of water = 24.5 * 9.81 = 240.345 kN
2. Calculate the weight of the masonry:
Volume of masonry = (1.5 + 5) / 2 * 7 * 6 = 199.5 m³
Weight of masonry = 199.5 * 21.6 = 4314.48 kN
3. Calculate the maximum pressure intensity:
Maximum pressure intensity = 240.345 + 4314.48 = 4554.825 kN
Therefore, the maximum pressure intensity at the base of the dam when it is full is 4554.825 kN.
Now, let's move on to calculating the minimum pressure intensity at the base when the dam is full.
The minimum pressure intensity occurs when the water level is at its maximum, i.e., 1 meter below the top of the dam. In this case, only the weight of the masonry contributes to the pressure.
Minimum pressure intensity = Weight of masonry
Calculating the minimum pressure intensity:
Minimum pressure intensity = 4314.48 kN
Therefore, the minimum pressure intensity at the base of the dam when it is full is 4314.48 kN.
Please note that these calculations assume uniform density and neglect any additional loads or factors such as hydrostatic pressure.