Apart from inertia force, which of the following forces is most important in motion of submarines underwater?
Assuming that the thrust T of a propeller depends on the diameter D, speed of advance V, angular velocity ω, dynamic viscosity μ and mass density ρ, which of the following ’non -dimensional parameters can be derived ‘by dimensional analysis?
Number of variables = 6
Number of dimensions = 3
Dimensionless parameters = 6 - 3 = 3.
Take D, V, and ρ as repeating variables.
VD/μ will not be dimensionless- number as its dimension is [M-1L3].
Which of the following could be a π-parameter of the function f(F, V, r, m, L) = 0 when V, r and L are taken as repeating variables?
A π parameter is constant and has zero dimensional unit i.e. M°L°T°.
Match List-I (Flow problem under study) with List-ll (Model law) and select the correct answer using the codes given below the lists:
1. Rise of gas bubbles in liquid
2. Flow of gas in a pipe
3. Flow over a spillway dam
4. Flight of supersonic jet
A. Euler number
B. Froude number
C. Mach number
D. Reynold’s number
E. Weber’s number
A ship’s model of scale 1 : 100 had a wave resistance of 1 kg at its design speed. The corresponding wave resistance in prototype will be
Froude model is applicable here because of influence of gravity force using froude model law,
or, Fp = 1000000 kg
If the velocity, bulk modulus of elasticity and the mass density of a fluid are denoted by U, K and ρ respectively, then the Mach number is given by
Mach number U/C =
Euler’s equation of motion
max = (fg)x + (fp)x + (fn)x + (ft)x
→ Reynold’s equation
fg → Due to gravity
fp → Due to pressure
fn → Due to viscosity
ft → Due to turbulence
max = (fg)x + (fp)x → Euler’s equation
(Neglected viscous force vand force due to turbulence)
A model of reservoir is emptied in 10 minutes. If the model scale is 1:25, the time taken by the prototype to empty itself, would be
∴ tp = 5tm = 5 x 10 = 50 min
When Mach number is more than 6, the flow is called
when the Mach number in flow region is slightly less to slightly greater than 1, flow is transonic flow.
A harbour model has a horizontal scale of 1/150 and a vertical scale of 1/60. The interval between successive high tides in the model will be nearly