Final answer:
The diameter ratio of the jets in the impulse turbine blade is 4:1.
Step-by-step explanation:
To determine the diameter ratio of the jets in the impulse turbine blade, we need to compare the velocities of the jets. Since each jet produces a velocity of 100 m/s, we can calculate the diameter ratio by comparing the areas of the jets which is proportional to the square of the diameters.
The formula for the area of a circle is A = πr², where r is the radius (which is half of the diameter). So, if the velocity is the same for each jet, the area of each jet will be the same.
Let's assume the diameter of the first jet is D, then the diameter of the second jet would be 2D, the diameter of the third jet would be 3D, and the diameter of the fourth jet would be 4D. Since the area of each jet is the same, we can write the equation:
π(D²) = π((2D)²) = π((3D)²) = π((4D)²)
Simplifying this equation, we find that D² = (2D)² = (3D)² = (4D)². Solving for D, we get D = 4.
Therefore, the diameter ratio of the jets is 4:1, which is option a.