00:01
Let's solve question number 81.
00:03
Here the area of rounded orifice is given as a is equal to 25 mm square.
00:10
25 mm square.
00:12
Initial volume of air in tank, v note is equals to 5 meter cube.
00:18
And total volume of tank, vt is equals to 10 meter cube.
00:23
Press in initial pressure, p note is equals to 1 megapascal.
00:29
So we will draw the figure.
00:33
This is the tank.
01:03
So this is figure here this is vt total volume and now the vt is this this is pressure initial pressure p note this is pressure p this is area a now this is the volume flow this is pressure p and this volume is v note v note now applying the bernoulli equation between the liquid surface and the orifice we can write p divided by row plus v square divided by 2 is equal to p atm divided by row plus v v jett square divided by 2 where v z is 0 this term is 0 hence from here we can write vz is equal to root square root of 2 multiplied by p minus p aetm divided by 2 divided by row or we can rewrite it as root over 2 p divided by row as p atm will be 0 gauge now the mass flow rate of the water leaving the tank is m m dot is equals to row a vz which is equal to delta a multiplied by root over 2 p divided by row row a sorry this is row a divided multiplied by under root 2p divided by row from here we get mass flow rate m is equals to square root of two square root of two two p row two p row multiplied by a now the rate of change of mass in tank can be written as dm divided by d t is equal to del divided del t integration of row d v or we can write it as dm divided by d t is equals to row w multiplied by dv divv divided by d t it can be written as minus row w multiplied by d t note note v t is equal to vt is equal to air plus vw now for isothermal flow we know for isothermal flow isothermal flow we know p divided by row is equal to r t is equals to p note divided by row where row is equal to density is equal to mass of air divided by volume of air.
04:46
Now air density p into v is equal to p note into v note or from here we can write p is equal to p note v note divided by v now from continuity equation from continuity equation continuity equation, we can write row w dv, w divided by d t, plus m dot is equal to 0, minus row w dv a.
05:23
D .a .r.
05:25
Divided by d t, plus m dot can be written as square root of 2p, row w .a, a...