1. If Vis a velocity, a length, and v a fluid property (the kinematie viscosity)

Question

1. If Vis a velocity, a length, and v a fluid property (the kinematie viscosity) having dimensions of 12T-, which of the following combinations are dimensionless (a) Vev, (b) Ve/v, (c) V v, d) V/ev? 2. The volume rate of flow. 0. through a pipe containing a slowly moving liquid is given by the equation where R is the pipe radius, Ap, the pressure drop along the pipe, ? a fluid property called viscosity (FL-T), ande the length of pipe. What are the dimensions of the constant ?/8? 3. A tank contains 500 kg of a liquid whose specific gravity is 2. Determine the volume of the liquid in the tank 4. A liquid when poured into a graduated cylinder is found to weigh 8 N when occupying a volume of 500 ml (milliliters) Determine its specific weight, density, and specific gravity

Explanation / Answer

1) dimension of velocity = LT-1

dimension of length = L

dimension of kinematic viscocity = L2T-1

Dimensionless quantity from the given options is Vl/v . Option (b) is correct

2) pi/8 is a dimensionless quantity because pi and 8,bioth are numbers and hence dimensionless

3) density of liquid = 2000 kg/m3

mass of liquid = kg

volume of liquid = 500/2000=0.25 m3

4)weight of liquid = 8 N

volume of liquid = 500 mL=500*10-6 m3

specific weight = 8/(500*10-6)=16000 N/m3=16kN/m3

density of liquid = 16/9.8=1632 kg/m3

specific gravityof liquid = 1632/1000=1.632

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