1) Two large vertical plates parallel to each other are 2mm apart. A thin flat plate of 1 mm thickness,0.6 m*0.6 m size and 25 N weight is towed vertically up b/w the two large plates with a velocity of 0.2 m/s. the inside plate is equidistant from the two stationary plates. The gap b/w the large plates is filled with oil of viscosity 1.6 poise. Calculate the vertical force required to tow vertically upward.
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To calculate the vertical force required to tow the flat plate vertically upward, we need to consider the fluid friction acting on the plate. The vertical force required can be determined by considering the drag force acting on the plate as it moves through the oil between the large plates.
To find the drag force, we can use the formula for viscous drag force:
Drag Force = (6 * pi * viscosity * velocity * projected area) / distance
In this case, the viscosity of the oil is given as 1.6 poise, which can be converted to Pascal-seconds (Pa·s) as follows:
1 poise = 0.1 Pa·s
So 1.6 poise = 0.16 Pa·s
Next, we can calculate the projected area of the plate, which is the area of the plate that is perpendicular to the direction of motion. Since the plate is thin and being towed vertically, the projected area is equal to the area of the plate:
Projected Area = length * width
Given that the plate has a dimension of 0.6 m by 0.6 m:
Projected Area = 0.6 m * 0.6 m = 0.36 m²
The distance between the two large plates is given as 2 mm, which needs to be converted to meters:
Distance = 2 mm = 0.002 m
Finally, we can plug these values into the drag force formula to calculate the force required. Let's assume gravity is acting downward, so the force required will be the sum of the weight of the plate and the drag force:
Force Required = Weight + Drag Force
To find the weight of the plate, we can use the formula:
Weight = mass * gravitational acceleration
The mass of the plate can be calculated using the formula:
Mass = density * volume
Since the thickness of the plate is given as 1 mm, which is equal to 0.001 m, the volume of the plate is:
Volume = length * width * thickness
Volume = 0.6 m * 0.6 m * 0.001 m = 0.00036 m³
The density of the plate is given as 25 N, which is actually the weight of the plate. We can convert this weight to mass using the formula:
Weight = mass * gravitational acceleration
Mass = Weight / gravitational acceleration
Given that the gravitational acceleration is approximately 9.8 m/s²:
Mass = 25 N / 9.8 m/s² = 2.55 kg
Now, we can calculate the drag force using the formula mentioned earlier:
Drag Force = (6 * pi * viscosity * velocity * projected area) / distance
Drag Force = (6 * pi * 0.16 Pa·s * 0.2 m/s * 0.36 m²) / 0.002 m
Drag Force ≈ 13.61 N
Finally, we can calculate the force required:
Force Required = Weight + Drag Force
Force Required = 25 N + 13.61 N
Force Required ≈ 38.61 N
Therefore, the vertical force required to tow the flat plate vertically upward is approximately 38.61 N.