Question

A horizontal pipe carrying water tapers from 200mm diameter
at point A to 100mm diameter at point B. If the volume flow
rate is 55 litres/second find the pressure difference between
the points A and B neglecting any losses in the pipe.​

Answer 1

Answer:

Delta pressure = 45938[Pa]

Explanation:

This is a classic bernoulli equation problem, but first we must find the velocity at both ends of the pipe, knowing the diameters of each end.

$Q=V*\frac{\pi*d^{2} }{4} \\where:\\V = velocity[m/s]\\d = diameter [m]\\Q = volumetric flow[m^{3}/s]$

$Q=55[\frac{Lt}{s}] * \frac{1m^3}{1000Lt}\\Q=0.055[\frac{m^3}{s}]$

Now we can calculate the two velocites VA and VB

Using the bernoulli equation we have:

$P_{A}+ro*V_{A}^{2} +h_{A}*g*ro = P_{B}+ro*V_{B}^{2} +h_{B}*g*ro \\as we have the same elevation\\h_{A}*g*ro = h_{B}*g*ro\\Therefore\\P_{A}+ro*V_{A}^{2} = P_{B}+ro*V_{B}^{2}\\P_{B}- P_{A}= ro*V_{A}^{2} - ro*V_{B}^{2}\\\\P_{B}- P_{A}=ro*(V_{A}^{2} - V_{B}^{2})$

Where ro = density of water = 1000[kg/m^3]

$P_{B}-P_{A}= 1000*(7^2-1.75^2)\\P_{B}-P_{A}= 45937.5[Pa]$