Fluid Mechanics

Step 1: Reynolds number formula.
Reynolds number is given by the formula: where: - is the density of the fluid (assumed to be water, ), - is the flow velocity, - is the diameter of the pipe, - is the dynamic viscosity. Step 2: Convert units.
We need to convert the given values into consistent SI units: - , - , - . Step 3: Substituting the values.
Now, substitute these values into the Reynolds number formula: Step 4: Conclusion.
The Reynolds number is approximately . The correct answer is (3) 5091.

Step 1: Understanding the situation.
When a container with gas is moving with acceleration, the pressure distribution within the container will be influenced by the inertia of the gas molecules. The gas molecules at the rear of the container experience a force due to the acceleration, which causes the pressure at the back to be higher than at the front. Step 2: Pressure distribution due to acceleration.
In an accelerated frame, the pressure at the back plane will be higher compared to the front plane because the gas molecules in the front part are subject to less pressure due to their inertia opposing the acceleration. Step 3: Conclusion.
The correct answer is (3) less in the back plane.

Step 1: Understanding the situation.
The ice thickness is given as 20 m, which means that the depth of water under the ice is 20 m. To lift a bucket full of water, the rope needs to cover the distance from the top of the ice to the bottom of the lake. Step 2: Minimum rope length calculation.
The minimum length of rope needed is the sum of the thickness of the ice and the distance to reach the water under the ice, which is 20 m. Hence, the rope required is the same length as the ice thickness: . Step 3: Conclusion.
The correct answer is (4) 9 m.