In the experiment for measurement of viscosity \( \eta \) of a given liquid with a ball having radius \( R \), consider following statements:
A. Graph between terminal velocity \( V \) and \( R \) will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \( \eta \) will change.
Analyze each statement.
A: Incorrect, as the graph is not a parabola but rather a more complex function of radius and viscosity.
B: Incorrect, as terminal velocity varies with ball size and density.
C: Correct, as viscosity and terminal velocity are temperature-dependent.
D: Correct, as variations in terminal velocity can reflect differences in liquid density.
E: Correct, as the initial speed affects the drag force and settling time, influencing the measured viscosity.
A cube of side 10 cm is suspended from one end of a fine string of length 27 cm, and a mass of 200 grams is connected to the other end of the string. When the cube is half immersed in water, the system remains in balance. Find the density of the cube.
In a low-speed airplane, a venturimeter with a 1.3:1 area ratio is used for airspeed measurement. The airplane’s maximum speed at sea level is 90 m/s. If the density of air at sea level is 1.225 kg/m³, the maximum pressure difference between the inlet and the throat of the venturimeter is __________ kPa (rounded off to two decimal places).
In a fluid flow, Mach number is an estimate of _________.
Consider a pair of point vortices with clockwise circulation \( \Gamma \) each. The distance between their centers is \( a \), as shown in the figure. Assume two-dimensional, incompressible, inviscid flow. Which one of the following options is correct?