1. Each dimensional formula is in which form?
Explanation: Every dimensionless formula is represented as the function of the [MLT], where M is the mass, L is the length and T is the time.
2. The exponents of the formula can be _____
a) Only positive integers
b) Any Value
c) Only Fractions
d) Only Negative
Explanation: All the exponents can be (α, β, ¥) integers either positive or negative and can also either be fractions or zero.
3. Flow rate can be expressed in dimensional formula as ____
Explanation: The flow rate can be expressed as Kg/s i.e. [Q] and hence [Q] = M/Ө = MӨ-1.
4. On which of the listed, Reynold Number of flow depends upon?
a) Capacity, Mass and Diameter
b) Diameter, Length and Capacity
c) Diameter, Velocity and Viscosity
d) Velocity, Capacity and Pressure
Explanation: The Reynolds number can be expressed as [DVP/U], where D is diameter, V is the velocity and P is taken as to be density and U is the viscosity.
5. Pressure drop can be dimensionally written as ____
Explanation: The pressure drop can be written as kg/m2 as it is also same as force thus dimensionally [F/L2], where F is the force and L is the length.
6. For Rayleigh’s Criteria, Minimum number of unrestricted components are ___
Explanation: The number unrestricted components for Rayleigh’s Criteria is (n-r-2), where n = number of quantities and r is the primary dimensions.
7. The dimensions of density is?
Explanation: The units of density is kg/m3, hence the dimensions can written as M for mass and L raised to exponent (3), Thus [M/L3].
8. The working rule for the Buckingham π method is?
Explanation: Langhoar has proved that for a number of dimensionless groups ‘P’ constituting a complete set for ‘n’ quantities is given by p=n-m.
9. The ‘P’ dimensionless groups are related as ____
a) Φ (π1, π2, π3, π4…) = 0
b) α (π1, π2, π3, π4…) = 0
c) β (π1, π2, π3, π4…) = 0
d) µ (π1, π2, π3, π4…) = 0
Explanation: The ‘P’ dimensionless group are related to π1, π2, π3, π4… by the general formula as suggested by Buckingham.
10. What is the maximum value of m?
Explanation: The maximum value of primary dimension that are (FMLӨT) is 5, these are fixed and hence cannot be changed.